Question about accident today

Today I got in a minor car accident. Driver (myself) and my passenger are okay, but car is damaged. Basically, I turned into my apartment complex at a very low rate of speed and because it was a complete sheet of ice, my car just started drifting and crashed into the curb. The drivers side front tie rod is definitely broken and I think the steering column is also damaged/ disconnected. My question is, would be apartment complex’s insurance (property/liability/?) be liable to pay for this? They rarely plow and never salt the road. This patch of ice is pretty perilous, and especially coming off a major road where often people are riding your ass and occasionally even rear end you when you are turning into the complex, it seems like they could be held liable for damages caused here.

Thoughts/ advice? I have the money to pay for the repair (or pay cash for a new vehicle if the repair exceeds what I’m willing to spend) but obviously since I truly don’t believe I am at fault for this I’d prefer to find a way for them to cover it.