I use to ride through the winters without any eye wear at all, and only only very fast descents did it bother me. And even then, I would just blink a lot and be fine not even a second later. Now I use glasses and have no problem. On some fast descents I still can get watery eyes, but it's for only a second.

I think it's unnecessary to buy another set of "winter eyewear", my normal pair works fine.