we just did a stay on the mountain type of trip. $20 a night per person. just a small cabin in a bowl. woodheat, propane cook top, led sting for lights. you can make it as cheap or expensive as you want. this place was a ski associaton hut. don't know why you coudn't do it for sledders. there was no caretaker or anything like that. Outhouse, pack yourstuff in and pack yourstuff out.
you don't need big lodges with 5 star dining to stay on the mountain. roof, heat and food.
I do believe the biggest obstacle would be fuel.