When I was in the US, most winters were still ok for caching. As long as the snow wasn't too deep, you could usually still find a few. It was only a rare occasion (as shown in my picture) that the snow got too deep to make a real attempt at finding the cache. I recall several hikes miles deep into the woods in 1-2 feet of snow just to find a cache.I personally am a big baby about being cold and do not like to venture out in it. I find winter is a great time to work on solving puzzle caches, make swag and work on creative containers. I also like playing the Cache me if you can board game from DPH games. It's a lot of fun. My kiddo and snuggle muggleenjoy it too.
However, since moving to Estonia, we get freezing temperatures for months, with strong winds coming off the sea and lots of snow. I have tried some winter caching here, but usually just give up because it is too cold and/or the cache is buried or even frozen in place. Now, if I go caching it is usually in fair weather.