Suggestions for winter cycling glasses?
Look for downhill MTB goggles.  These will be made to fit with a standard bike helmet and will have sticky plastic on the straps so that they will stay in place on your helmet.  I rode with a pair last winter and was very happy with them.  Kept my eyes warm and didn't fog even under heavy riding.  Many also come standard with clear lens so visibility won't be an issue.  



Link - Note these arn't the pair I have - just did a quick search and posted the first pair I found.  I am not endorsing these goggles or the company selling them.