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.
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.