Some great advice here. The only things I think are worth adding are:
It's not just about how warm your clothes are, dressing in layers would be highly recommended. It gives you a full range of flexibility for all weathers. And each layer deals with a different issue (sweat, insulation, protection from wind/rain).
Stay hydrated. It's quite easy to remember to take on lots of fluid in hot climates. But it's quite easy to forget in cold climates. So it's worth considering trying to kill two birds with one stone and take a thermos with something hot as it will be both hydrating and warming.
Keep taking on calories. You burn a lot of energy in the cold, especially when you're active. Snacks are a must, and don't feel guilty about taking something that's really fatty or sugary!
Useful references:
https://www.rei.com/learn/expert-advice/layering-basics.html https://www.summitmedicalgroup.com/news/living-well/stay-hydrated-cold-weather/ https://effortlessoutdoors.com/winter-camping-how-to/