The best option for clothes is layers. Something the water and wind won’t get though, so goretex is best. You don’t need anything to heavy either if you buy good stuff. After doing the first pitch ice climbing myself and the first guy were sitting on an ice ledge waiting for the third guy to climb up. First guys outer layer was covered in a layer of ice with the last patch melting in the car that was 45 minutes away so the ice probably lasted about 2 hours if not longer. They weren’t even bulky thick outer layers. I probably had more bulk from my regular ski jacket and less warmth. His pants where also less bulky and I’ll bet his legs were just as warm. You just need good layers so that you won’t sweat while your active but you have something to throw on for that little bit extra warmth. A pretty thin insulated jacket is basically what they had and it was pretty valuable for the weight it added on the pack which I doubt felt like much. Depending on the weather you’ll be experiencing you might need a thick parka but that depends on how cold you expect it to get. Nose hair freezing ?
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.