I live at 7000 feet and have snow and sometimes-30 below zero F. My three horses get fresh hay twice a day, grain in the morning and alfafa pellets at night. They also have 2 75 gallon water tanks, both are heated, I have to drag a hose to fill the water troughs and bring them back inside the house to keep them unfrozen. Horses can't survive on snow, they would have to eat gallons and gallons of cold snow to even begin to have enough water, because they are eating cold snow, it is even worse. As far as hay, they need hay to keep them going while digging through snow to get at whatever is underneath. Whatever is left underneath has absolutely no food value, like eating straw.
I work for a vet and during the winter we see horses almost everyday with blockages and colic due to eating snow for water. I live in a valley where the oldtimers still feel a horse can eat enough snow to keep their water needs up. Not true. It is very very important that horses have clean water to drink, up to 7 gallons a day per horse.
As far as shelter, alot of states don't require shelter and won't even be worried about horses being made to eat snow. Our state doesnt require shelter for animals and if you turn someone in, if they see signs of any hay and there is snow on the ground, they are happy.