I do deliberate trail maintenence regularly, and unfortunately what you can do is severly limited if you want to do it casually while only carrying something small.
There is no set of tools you can reasonably carry, even if you go out only for that purpose, that will cover more than maybe 3/4 of the problems you find. My preferred weapons for deliberate trail maintenence are work gloves with leather palm and palm-side of the fingers, a bow saw, and a small pair of clippers. The clippers are the kind you can work with one hand. This is a tradeoff, but gives you good coverage for most problems up to where a chainsaw would be needed.
The problem with bringing more than one tool is that you constantly have to keep switching the tool you are using, and therefore have to put the other tool where you can find it again and won't forget it. The bow saw is relatively light and easily carried in one hand. I don't want something in the other hand, else I'd always have to put it down when using the bow saw. That's why I bring a small pair of clippers so I can keep them in a back pocket.
A bow saw is probably the single best tool. You may be surprised what you can cut with it. White pines (Pinus strobus, the easiest trees to cut here in New England) up to 6 inches can be handled. Oaks and harder wood up to 4 inches without too much trouble, and 6 inches if you're willing to spend some time and put some effort into it. That means multiple cuts to make a notch, probably from both sides. With a pine, in contrast, you make a small cut on one side, 1/3 of the way thru from the other, and then just push it over. Downed limbs is more work but the same sizes can eventually be handled.
Other useful tools are a long pair of loppers, the kind it takes both hands to operate. However, if you've got one of those, you really can't do much else. This only makes sense therefore if you're in a group. Me with bow saw and small clippers, one person with large clippers, and one with a chain saw is a pretty good team. You can get more fancy, in some cases by adding someone with a rake or something that can rearrange dirt in the right conditions, but in the general case I'd rather have a fourth person have just "bare hands" (with good work gloves on, or course). A good part of the time you're just breaking things off with your hands, moving logs out of the way, or are dragging something off the trail that was just cut.
For me at least, I rather either go out to work on the trail or to hike. Each would significantly impact the other, so it's more trouble than it's worth in my opinion. I also regularly do trail work, so I don't feel bad at all about just going out and hiking and leaving the maintenence to someone else occasionally.
If you really want to do some maintenence while hiking without carrying much or taking much time, you're going to have to realize up front you're only going to fix a small part of the problems you encounter. I can see three levels of "casual" trail maintenence while the main point of the outing was just hiking. In order of seriousness:
- Bare hands. Wear a good pair of work gloves and do what you can. This has the advantage that you don't have to carry extra tools, you're always "ready", and you do a lot without even stopping. If you've never done trail work, you'll probably be surprised how much you can actually accomplish with "bare hands", suitably gloved so you don't think twice about grabbing a rough piece of wood hard and yanking and throwing it. A whole bunch of maintenence is simply clearing relatively small stuff that has broken off trees and fallen onto the trail. Remember that when dragging larger branches, drag them trunk-end first else they get hung up on everything. Think of them sortof as one-way ratchets.
- Add small clippers to the work gloves. You'll probably keep the clippers in the pocket and do bare hands things most of the time, but sometimes clippers are just what you need to deal with encroaching branches. Two rules to remember:
If in doubt, cut it out!
Inexperienced trail maintainers tend to cut branches right at the edge of the trail. Think about it. Trees grow, which is why the branch is now over the trail in the first place. Are you going to come every week and trim the branches back? I didn't think so. Think a few years out. If the branches from a 30 foot tree 3 feet from the trail are getting in the way now, think what will happen as soon as you leave after trimming them. If the tree is only 3 feet from the trail, cut the whole branch right at the trunk and you won't have that problem again. If it's a 10 foot tree, lose the whole tree. Problem permanently solved. Don't be timid. The trail is a small path thru big woods. Cutting branches back to 10 feet instead of the 5 foot trail width isn't going to hurt the forest, but it will keep the trail clear another two years longer, at least from that tree.
Never put a small hand tool on the ground
You may be tempted to put a tool down "just for a minute" while you use a different tool or drag off a branch or something. Don't. Put it in your pocket. Sooner or later you're going to forget to pick it up. When you come back to look for it, you'll suddenly realize how small the tool and how big the woods are. Unless you remember exactly where you put it (and you won't), it's gone.
I've even "lost" my bow saw for a while a few times, and that's much bigger than a small pair of clippers. I can't put the bow saw in my pocket, but I do have to get it out of my hands regularly. I make a special discipline out of deliberately putting it in the middle of the trail a bit further in the direction I will be going. That way, it's easier to find because the trail is presumably more clear, and if I forget I'll more likely notice it when continuing on.
- The last level of causal trail work while otherwise hiking is one of those folding saws. They are actually pretty crappy saws and nowhere near as effective as a bow saw, but they do work and will be the only way to cut something too big or tough for small clippers. That would be a white pine maybe 3/4 inch in diamter or something harder 1/2 inch.
Anything more effective than these three levels requires a more serious commitment to maintenence such that I wouldn't call it hiking anymore.