You are correct: Mittens work better than gloves, but are usually harder to find. The best mittens come as separate outers and inners.
They dry much faster at the end of the day.
If they soak through, you can change inners.
The outers are snow proof. In really cold weather I prefer nylon outers. Close to freezing, leather will keep your hands dryer.
For inners you can use either wool or fleece. On moderate days you can use knit or fleece gloves as inners. If you are working hard, often wearing outers with no inners works well. Flexibility.
Layering in general: Good idea. The layers depend on how cold it is, and how active you are. Warm still day (-5 to -10) snowshowing, I'll wear running shorts over polypro bottoms, and a windbreaker over polypro top. Take the sun away, or add any wind, and I'll add a light fleece between polypro top and that wind layer.
Sunshine makes an effective difference in the way you dress by about 10 C.
The wind chill charts are made by some obscure process that is more or less meaningless. The first 5-10 km of wind make the most difference. My rule of thumb is that for the first 10 kph, take off 1 C for each k. After that take off 1 k for each 5k. At one point Canada reported windchills in watts/square meter -- how much power did it take to keep a can of water at body heat. This correlated very well with how to dress. 1200 W/m2 meant jacket and toque and something on your hands unless you were splitting wood or running. 2000 W/m2 meant parka, fleece, poly and wind pants, balaclava. 2700 W/m2 (coldest I've been) required parka, light and heavy fleece, fleece pants between the poly pro and wind pants, double toque, scarf over the face unless the wind was behind you, your best fleece mitts inside nylon outers, with careful attention to overlaps. If you had to do anything with bare fingers you had about 10 seconds before they were too numb to use.
In general you want a wicking layer (polypro) and most of the time a wind layer (nylon) as it gets colder you add layers between them.
Acrylic (fleece) and wool are best. Acrylic doesn't hold much water. Wool stays reasonably warm even wet. Cotton is terrible wet.
Layers should be loose. Trap an extra air layer between them. Layers with separate functions are more versatile, generally easier to dry, and to clean. Buy a wind parka, not a winter parka. You can use a wind parka with different insulation all year.
I've found that a wind layer is more important than an insulation layer. A simple nylon shell zipped close will keep you warm when a loosely knit fleece will not.
Waterproof breathable fabrics
Avoid waterproof outer mitts, unless you are working with wet. They have serious condensation issues. This is where you will really want multiple sets of inners. Waterproof breathable doesn't seem to work at very cold temperatures. But at very cold temperatures water is not a liquid.
Waterproof breathable is an acceptable compromise in a wind parka -- you can open it up when you are warm, and it will vent fast enough to keep you dry.
If used for pants, you want good vent zippers to keep from soaking up. Your leg muscles generate a lot of heat. I don't use WB pants unless I'm working with wet snow, or rain or sleet.
Do NOT use for footwear, unless you are going through puddles. Duck shoes (bottom 1-2 inches rubber) work in spring or fall, but in full winter you get major condensation then cold toes.
Pants: Wear tops outside your foot wear. Don't tuck in. Snow will find it's way inside. This also allows you to tie the tops of boots loosely. This will pump some air in and out with every step, and slow down moisture collection in your socks.
Mitts: When not working (just walking, or using a ski pole) you want the back end of the mitt to allow some air exchange. This reduces condensation in your mitts. (Your hands sweat all the time. That water has to go somewhere.) Good outers have a velcro closer to secure them more tightly when the weather warrants. Again: Adjustable venting gives you more control.
If your hands are cold, put on your toque (watch cap, stocking cap, brain blanket...) Ditto feet. I buy cheap acrylic ones at the dollar store, because I lose them. Having a balaclava, (ski mask) for really cold days is good. Your body will reduce circulation to peripheral bits (fingers, toes) to keep the core warm. Putting a toque on reduces heat loss through your heat, so your body opens up blood vessels to the hands and feet.
For really cold weather, a parka is a good investment. Try to find one that the hood is sewn, not zipped. A: You can't lose it. B: no air leaks. Hood up, but partially unzipped allows slow flow through ventilation that keeps you dry.
Adjust to the circumstances:
Very cold: Add a layer underneath. Put your hood up.
Warm: throw your hood back.
Warm: Take off you toque.
Warm: Remove mitts.
Cool: Put your wind layer back on.
On an outing it's common for me to add or remove a layer, unzip or zip up, every few minutes. At one extreme, at -45 C with a 20 kph wind, I had my parka over sweater over fleece over polypro, double toque, hood up. Windpants over fleece over polypro, and was still cold. At the other extreme I've had moccasins polypro bottoms, running shorts, and no shirt mushing a dog team over hummocks.
Footwear: Don't stuff more socks than will easily fit. Most cold climate people have winter boots and the rest of the year. Winter footwear should have room for 2 pair of thick socks, or should come with felt liners. The felt liners become mandatory below -30. Purpose built winter boots are already sized larger to account for this. If you want to use regular boots or shoes for winter, be ready to buy them two sizes larger. But try them out with extra socks, and ask for wide sizing if they have it.
Runners can be used in winter if you can get enough socks in them. New Balance has runnings in double E and quad E widths.
If you are out of sight of your car, carry extra stuff. I carry 1 layer more than the worst I expect to wear. I also take a change of socks (in case I break through the ice on a creek or beaver pond)
If you are cold. Eat. Drink (not booze). Fuel up.