Reiterating much of what others have said. Some of these are more a preference than fact but...
Socks: Wool beats cotton, hands down.
Leave discs outside for a few hours before if you can - snow sticks to warm discs.
Layers for sure. Invest in a quality, lightweight, warm, base layer. Really make a difference. A base layer, then lightweight fleece covered up with a hoodie keeps me warm down to the upper 20's if its not too windy. Below that, I add a good softshell windbreaker as a 4th layer.
Avoid cotton next to your skin. Once you get going, you can start to sweat even in single digit temps, especially on hilly courses with a reasonably heavy backpack. Once cotton starts to absorb sweat, you'll have wet clothing on next to you with no air circulation because of outer layers - uncomfortable to say the least.
I keep hand warmers in the big pocket on the front of my hoodie. I prefer the
large Hot Hands Super Warmers, to their regular dual pack hand warmers. One of the larger size generates more heat stays warm longer than a two of the small ones, and they stay in my hoodie pocket much better.
Gloves vs. mittens, vs flip-top gloves vs bare hands... really is a matter of personal; preference, each with pros/cons.
Tried all of those. I 've found that super cheap (like $1 pair), knit poly gloves work for me. The kind of crap you might see on an end cap at Target or Walmart, at a convenience store, or even at a dollar store. I'm sure some folks would hate playing with them, but not me. I find I get good grip and still have a decent "feel" for driving and putting, but I think I'm probably in the minority there. I never have to take them off during a round, which is convenient.
For deep snow, I put my bag in one of those cheap, plastic, sleds for kids, and pull it behind me. Easier than taking my backpack on/off repeatedly, and the resulting snow on my bag, and subsequently my clothing.
I'm a fan of ribbons when there's more than a couple of inches of snow - again preferences vary greatly on on that.