Accident with workshop car

Hello!! I gave my car for repair yesterday and got a replacement car from the workshop. I didn’t have to sign anything, no costs, etc… Unfortunately the vehicle had already summer tires on it, what they told me. End of story: Temperature drop, suddenly snow/ice on the road. Brake path far too long. In order to avoid a violent crash, I left the road to the right and crashed against a tree ->Total damage. The car was not fully insured by the workshop. Someone now has to cover the costs. (>10,000€) Can I be prosecuted now? Officially, I’m to blame (who else, of course), on the other hand, it wasn’t my car and I hope the car dealership is responsible for the insurance of its fleet itself… My workshop is just as shocked as I am and has not yet commented on this matter. soon get mail. Try it pretty sure. Who has to pay for the damage now? Workshop, me, both??? I would be very grateful about a short info. I am really not an expert in such stories. Thank you in advance. Greeting Michi