Kitty, maybe I am looking at this wrong but your profile says you are in Texas. Where is ski season in Texas? Would you have to take the little girl to New Mexico or Colorado to ski? Could it be that he doesn't want you to travel with her or if he had to go too that it would bring up too many hurts?
I can understand your desire to keep your promise but sadly, it is her father's decision to make. You can and should make the offer since you promised but in no way should you talk to the girl without her dad's permission. Even then don't say anything about him not letting you take her. It is not your place to put a wedge between them.
So ask. Try to do what you promised but don't worry if your offer is rejected.

KD