They may be at fault, but unless a cop sees it happen I seriously doubt you’re ever going to collect. Not like you can pull them over. And even if you do get them pulled over it’s just your word against theirs when the cops show up. If anyone every tried to claim that with me I’d just explain to the officer that my car was clear before I left and some asshole with a POS is trying to get me to pay to fix up his car.
Moral of the story… If you’re going to drive a car in winter keep a real good following distance if it’s covered in snow/ice, and keep a low deductible on your insurance.