My "snow boots" are LL Bean hiking boots with enough room for socks, since I'm walking a lot. My feet haven't gotten wet even walking through all the puddles and wet snow on campus for four years. (The hems of my jeans is another issue entirely. I like lph's rubber boot suggestion for that.)

I had snow boots, which were shearling-lined and mid-calf. Warm, but not enough grip for my taste.