Is This a Personal Injury Case?

An experienced skier is skiing a new mountain for the very first time. He skis down a run that should have been roped off or at least marked “off-limits” because of avalanche dangers and some dangerous drop-offs. After a little while, he decides to turn into the trees (he has done this several times before and never gotten hurt). But this time, his speed causes him to lose control and he hits a tree going pretty fast. He ends up with some broken bones and an expensive hospital bill but survives.

Does he have a winnable case against the ski resort for negligently failing to rope off the off-limits run, or at least put up a sign about it being off-limits due to the dangers?