How can I convince my parents to let me go skiing with my friends?

I went on a school sanctioned ski trip last year. The problem is this year, my schools not going skiing and my parents only let me go on school sanctioned trips because they can't ski or snowboard and if they took me skiing they would be in the lodge donig nothing and they wouldn't be able to see me and if i got hurt and i couldnt move or something they wouldnt know. I asked them the other day if I could go skiing with my best friend. Her parents know how to ski and my mom said no because she didnt want to put me into someone else's responsibility. Yes my parents are very over protective. Please help me!!! I have never scolded or yelled at my parents or done anything bad and they trust me its just that they dont want be to get hurt.