Be careful with how much policing you want. If you look at an average ski slope with a critical eye, 99.9% of users go roughly straight down the hill, with few paths crossing. Then there are a tiny % of users that dart and dodge all over the place, weaving back and forth at high accelerations.
Collisions can only happen when paths intersect. So it's simple: Paint lanes down the run, mandate turn signals, and ban turning.
This is said tongue-in-cheek, but I had a ski patroller tell me that I "came into his lane" years ago. Everyone is confident that their ideas are correct and it's everyone else that's the problem.