I can't imagine a ski resort being held liable under the conditions you set out.
Read your lift ticket.
But, go to a personal injury lawyer to see what he says about your case.
It could be binding IF it is otherwise legal under the state's child support laws.
That is the very general answer.
But you really have not given us enough facts, details, and info to give you a specific answer.
Go to the courthouse.
When you are in the courthouse, go to the office of the person who collects taxes on real estate.
When you are in the courthouse in the office of the person who collects taxes on real estate, ask whoever what address they use to send the tax bill to.