I think I could see nose hair freezing cold when stationary. I think I keep going for some magic bullet, but the answer is a more mundane "bring extra layers and add them if you get cold." I have just a generic multi purpose activity winter jacket I've used hiking. I've looked at the nicer jackets, the insulating layers and shells. For the cost, I'm never convinced I'm missing out. I probably paid less than $200, and the nice shells and warm layers seem to be $500 each.
If your feet are cold, put on a hat...I've found good headwear, base layers, and a hard/soft shell jacket (got a good Mammut one for ~$100 on clearance) are what works. And gaiters. Always have gaiters.
You should be able to get a nice goretex shell for like $300 max. I find my ski jacket to be pretty good for most things but I definitely would have been more comfortable in those fancy layers. Which brings me to another things, gloves or mitts. I have what would be considered great gloves but you have to be way to careful about not getting the inside wet. Not sure how much the mitts I wear now are because they were a gift but they’re definitely expensive and there’s a huge improvement. Marmot has some good stuff.