Rode 20 miles on snowy roads about an hour ago. Road riding in winter is definitely an option if you have a bike that can take a bit fatter tire. Hybrids, touring and CX bikes make great winter rides. We have lots of recreational riders and commuters out this time of year in the Fargo, ND area. It is entirely possible to ride on a variety of tires, especially if you are just riding in an inch or two of new fallen snow, but if you can invest in a set of studded winter tires, it will increase your safety and confidence on ice or hardpack all winter long. I don't switch to winter tires unless we have ice or a staying snow. If it is just the snow in the morning - melt by noon type of fluff we get in the fall, I just ride a bit more carefully until the road dries off. MTB on snowy trails is a blast as well. Whatever you do, DO NOT ride a fat bike in the snow. It's addictive and there is no treatment or cure. You'll know you are a real winter rider when you understand that a balaclava is not a Greek dessert.
What I like best about winter riding is that you can take a road or trail that you have been on 100 times and it is still a whole new experience.
A few shots from one of last year's winter rides.