In theory buildings in this (occasionally snowy) country should be built to cope with snow and if regularly maintained you should be fine. But as another poster on here had a bad experience with her horses having their roof fall on them it might be worth considering...
Be very, very careful though and make sure you're not alone if you do it as a fall is one thing but a fall into freezing snow you can't get out of is another!
Yard I was at had a lean to where the out horses are tied up and last winter the roof on that collapsed under the snow. Fortunately no one underneath it at the time. There wasn't a lot of support to it though and am sure most stables will have lots more.
We've had a large section of guttering come away from the stables because of the weight inside it. I had to get up with some hot water to try and thaw some of it out before we could lift huge chunks out of the gutters. Will have to wait until it all thaws out before doing any repairs.
The same thing has also happened to the guttering around the garage and the shed. Stable roofs thankfully okay.