I've got quite a few waterproof pants for some reason. I've worn them to football games in the rain and done some winter activities. However, all were pretty much bought at a discount or weren't terribly expensive.
For snow activities you'd probably want at least waterproof membrane with a thick nylon fabric and at least a mesh or nylon lining. I have a pair of pants I bought from The North Face at one of their outlet stores for $80. It uses a breathable polyurethane membrane called "HydroSeal" although it's been discontinued. That one is pretty nice since it has a zipper and Velcro on the sides where I can take it off if I've got something underneath. I've got unlined pants, but they're not suitable for real winter activities. They're good for packing and putting on if I have to trudge through rain. About the
best buy I've ever seen was a pair of black Gore-Tex pants from The North Face that I found in a clearance rack at a sporting goods store for $50. They were regular, full-warranty so I couldn't believe it. I tried them on and they fit great. However, an employee pointed out to me that they were a women's model. They didn't seem to be cut for women's hips and there was nothing on the outside identifying them as for women, so I bought them anyways. Next time I go play in the snow I plan on bringing them along.
And trust me that you want waterproof for the snow. I remember my one and only attempt to learn how to ski was wearing jeans. The instructor said that my friend and I would find it miserable. Whenever we fell, the snow would get on our pants and turn to liquid. At the very least not cotton. The ideal would be waterproof pants and non-cotton thermal bottoms. If it's not waterproof, avoid cotton.