Along the lines of nuliajuk, if it is just for the cold winter days, a cheap solution is to buy over-the-glasses (OTG) safety glasses. I bought some off the internet that aren't the big, bulky safety glasses you get from the hardware store, but instead just fit over my glasses.

One of these days I'll buy prescription cycling glasses, but I'm not convinced I can successfully purchase glasses over the internet (I know, I know, many do it without issue, but I've had problems with in-person purchase that I'm skeptical)