You go to the ski centre in your trainers/moonboots/bare feet if you like get your skis/boots on and leave your trainers moon boots in a pigeon hole, you then return youre skis/boots to the ski centre at the end of your ski session and put your other footwear on.
Good point - I must admit I never thought anyone would take my smelly old walking boots - wait until Pamp. Pete comes back to the site, perhaps there are some lockers at the snow shack. There must be for the staff perhaps