Running on snowy and/or icy roads has gotten a lot easier in recent years with the wide availability of traction devices you can attach to your shoes, such as YakTrax and STABILicers. They allow you to run with much more normal mechanics than would be the case in just your running shoes.
The first time I ran in YakTrax, I was dubious. My run was fine, and I certainly felt like my form wasn’t the usual slip-slidingaway phenomenon that can make running on snow so unenjoyable. But I wanted to be sure I wasn’t imagining things, so when I got home, I took off the YakTrax and then ran down my street in just my shoes. The difference was obvious. Now I wear them or STABILicers whenever I know the bulk of my run is going to be on roads that haven’t been plowed to the pavement. I’ve also worn them in the woods once I know trails have been heavily traversed by hikers and snowshoers, resulting in a firm surface. It’s a real treat to run on favorite trails at a time of year they would otherwise be inaccessible.
If you run on snowy roads without one of these traction devices, expect your hamstrings, especially at their insertion points below your butt, to be sore afterward. Your iliotibial bands are also likely to get aggravated from the extra work they’ll do to stabilize you with every step. Do some gentle stretching of those areas after snowy runs, and then apply ice for a few minutes to the top of your hamstrings.