I ride in the snow a lot and I use...fleece ball cap with ear flaps, you can find all over, and then clear ski googles over my perscription glasses. Go try some on and see what fits over your personal glasses, ski goggles are made to fit over ski helmets so they go over bike helmet fine. I like clear but I have purple ones also that work ok. Also, get an anti fog cloth for both goggles and perscription glasses as it helps keep the fogging down.
Your other option is sports goggles with your perscrption in them, expensive but if you ride in snow a good portion of the time it might be worth it.