To start with, there is no such "list" which can adequately cover your question- every trip is different, every scenario is variable, and winter is such a broad period that regions have completely different challenges ("winter" in the Northern Hemisphere happens in a different part of the calendar year than it does in the Southern Hemisphere, and January in the Front Range of the Colorado Rockies varies drastically from March in the same location varies drastically from the Western Slope 100 miles West). Additionally, hypothermia can easily be suffered in July or August (at 2000m elevation, in July temps can be under 10C at night, even start dropping in the 10-15C range by dusk).
The only constant item you will always bring with you is your brain; that may sound flippant or impudent, but I mean it quite sincerely. Going into the wilderness without proper knowledge and education is the first potentially life-threatening mistake you can make (you referenced not knowing how to erect improvised shelter). Next, if you lose your head and start to panic, you will be in a world of hurt; education is the foundation here.
Have you taken a Wilderness First Aid course? Are you aware that, if you require assistance by a Search and Rescue team, it can take over an hour just to transport you 0.75km (0.5mi)- not counting the time it takes to call them, SAR to organize and respond, response time, travel time to you, patient evaluation, patient package for transport, handoff to EMS personnel, transport to hospital? Do you know how to handle an injury in the backcountry and the exponentially complex nature of something as simple as a blister which wasn't managed properly when you are in the backcountry versus front country (e.g. your house)? Do you have a proper first aid kit and know how to use it?
Next is basic survival skills. This doesn't have to be an expensive class by any means. There are usually groups which will teach basic skills in wilderness survival and how to keep warm and dry.
As for gear, backcountry medicine and survival is 90% improvisation, so a good class will teach you goal oriented skills and how to improvise with the items you always carry. ab2 referenced trekking poles and I agree; I always walk with them (when I was a guide one of the guys on my team used to call them "wussy wands" and I love the term- especially since he now uses them). They will reduce strain on your back, knees and ankles and they are incredibly versatile- splints for instability in limbs/joints, improvised shelter building, etc. a base list might include (but is not limited to):
- Aforementioned trekking poles
emergency blanket (the heavy duty kind such as those made by SOL, not the cheap limar "space" blankets)
- Cravat (x4)
- SAM splint
- Fire starter (flint and steel and nesting material- practice and know how to use them)
- Signalling materials (I like the Silva Ranger compass with mirror and sighting slot, Storm(tm) whistle, and the flint and my fire building material is also for signalling)
- Navigation tools (manual, NOT your phone or GPS, and know how to use it- the compass serves double duty here, and carry a map of the region in which you a traveling)
- First Aid kit; a real one- no off the shelf first aid kit I've found is sufficient or effective. They're usually "150 parts" 145 of which are useless in the backcountry, or made for x number of people for y number of days and are way overpriced and full of a bunch of junk you won't use, missing stuff you need, and have a little first aid book which won't do you much good in an emergency ("let me see, you're bleeding out...bleeding..bleeding...ah! 'uncontrolled bleeding, what to do' page 18, 72, 101...okay..give me a minute to look that up..."). Take a WFA or WFR course, know how to use it and what to do.
This may sound like a lot and very expensive (and some may say overkill for a day hike), but the listed items actually aren't that substantial in size/weight and a day hike is something which seems like a simple activity which doesn't require more than shoes and a water bottle, but it can quickly become life threatening.
Permit me to relate an anecdote here:
A couple of students of mine were enjoying a day hike on a trail just outside Boulder, Colorado (about 30 minutes from the hospital) when, about 1.5mi (~2.4km) in they encountered a young lady on her way to the trailhead to call for help (they were in a canyon and reception was spotty). She said her friend had "fallen" and was hurt so, having recently completed their Wilderness First Aid course, had their first aid kits with them and went to check on her.
The patient had fallen 20ft (6m) from a rock and was in pretty bad shape. The two young ladies requiring assistance were on a simple day hike in July in a well known area close to town, and were taking a short break on an overlook to take in the view when the patient slipped and fell. it took 13 hours to get her to the hospital. They had no first aid training, no first aid materials (just hiking shoes, snacks and water) and no survival materials (shorts and t-shirts for summer weather). Worst of all, no training of any kind and so no ability to improvise with what they did have.
Luckily, the friend did have her cell phone, kept her wits about her, and knew enough to make sure her friend was breathing and went for help. They just got lucky in that some trained and well prepared people were on the trail ready to render assistance.
EDIT IN RESPONSE TO COMMENTS:
My apologies for not making the connection on the use of my anecdote clear- the point of the anecdote is to drive home the importance of training and the difference it makes to have someone with training versus being without, and illustrate how complicated it can be even with training. The reason for that one in particular- even though a summer example- is that the question was directly related to a day hike close to the front-country and people often minimize the necessity of being prepared with a solid first aid kit, but that it is a potentially fatal mistake to make.
As for cravats, their inclusion in my list is not a typo- in my opinion, they are the most underrated yet versatile item you can carry in your pack- build a shelter, stop bleeding, make a splint, improvise and you can come up with hundreds of uses. The reason for four is that, with four, I can effectively splint and package any limb fully and completely. Can I do it with less- sure, I don't actually need any, but they take up so little weight and space that, at $0.89, why wouldn't I carry four?
Regarding off the shelf first-aid kits, I have yet to find one which I wasn't, in the end, having to replace so much of the contents that I ended up using it for just the bag. They are made to make money- the contents, while great at home, are neither the quality nor are they of the type that I need in a good kit. I don't need a set amount of items, I need to change my kit depending upon which activity and duration I am doing. I need to change a dressing on a wound every 24 hours in the backcountry. Assuming I need to be prepared to handle wounds which may require a 3x3 gauze pad and a roller gauze to dress (not counting irrigation and infection mitigation), if I'm on a twelve day trip in the desert and I get a 4" laceration on my shin falling while setting up a rock climbing route on day two (happened to me), how much gauze do I need to be prepared with to manage that wound and prevent infection? Chances are, I won't have to dress it the entire time (in fact, I shouldn't if I don't have to) and bandaging, so long as it's clean, may be reused so I may not need to account for every day but, if I see signs of infection, I need to change it more often and keep it covered longer.
In this case, I was also one of the trip guides, so I'm carrying a larger kit due to the fact that I'm prepared not only to take care of at least 3 wounds for myself, but at least 3 from trip members (they are carrying their own too, but I need to be able to have materials ready at hand). Even so, For just this one wound, I have a pair of nitrile gloves, 3x3 gauze, roller gauze, povidone iodine wipe, and alcohol wipe for each for 11 days x1.5 (for infection) when I leave. A lot? sounds like it, but I'm not interested in cancelling a trip because I wasn't able to manage a simple wound. I also have that x5 (I've got enough for several wounds remember), plus material for a major bleed event, splinting material, sting/allergen material, signalling and TIH mitigation, etc. Sounds like my FA kit is as large as my trauma kit on the Engine in my station, but it isn't, it's broken into a few small kits, 3x3x4/5/6, placed in the voids in the top of my pack. For shorter trips or day hikes, it gets smaller based upon duration of trip and activity, all fits in a single small bag. No off the shelf has more than a couple of gloves, a couple gauze pads, maybe 1 or 2 roller guaze.
I can't get into wound cleaning and management here. I'm not teaching a wound class, so I won't get into the data on the benefits of wounds being left open and moist versus covered and dry, closure vs non, how to use povidone iodine and alcohol, when absolutely NOT to, what to use for irrigation and how, etc. I can't cover how to properly recognize wound infection, the seriousness of it in the backcountry (4, 8, 10, 18 hrs are the times to watch for it initially), highest risk areas of the body, etc. There is a lot there (few hours of class), not will I try- that's a hands-on class, and takes a lot of time. Thus, take a class in backcountry medicine and learn what you need to know to mitigate these things, how to manage them, and what it takes to actually treat and manage a wound, and you quickly begin to see off the shelf first aid kits in a whole new light (at least, I do- they are heavier and bulkier than mine, and lack the equipment I need to manage even a single wound in the backcountry).
It has been my experience that, the longer our trips get, the lighter we try to make our packs but the heavier our first aid kits, by necessity, will get. Can an argument be made that it's all overkill, totally unnecessary and you can get by with much less? Sure. It's called confirmation bias. Everyone has their own opinion on these things, and I'm not claiming to be an expert, I'm answering from my own experience from 30 years of recreational, guide, military, and rescue experience.