I think lots of people give milk with the snack but what we did was start giving her milk with meals, plus the bedtime bottle. So when she wakes we'd do breakfast and milk, snack with water, lunch with milk, snack with water, supper with milk and then the bottle before bed. Once she got used to this we slowly started offering her her milk in a sippy at meals. She would only have a few sips at first and we would then finish off with a bottle. Gradually she got the hang of the sippy and started to take more and more so we eliminated the bottle altogether with the bedtime one being the last change. It took about two weeks total. When she has water with her snacks we use a regular cup and we're hoping to do the same type of transition to get her to drink her milk out of this. Does this make any sense?
I hope it helps a bit... oh and we couldn't get dd to drink out of a sippy at all for the longest time even though she would take water out of a regular cup... one day she went to the cupboard she's "allowed" to open (with all the tupperware etc) and she just took her cup out and started to pretend drink. That's when we just went for it.
Good luck and I'd love to hear how you progress!
Sharon