She'll be fine as long as she's not clipped and is used to be outside with free access to the shelter.
5 - 8 inches of snow is nothing to a horse. I've gone riding in snow so deep that my feet dragged in the snow (bareback). Mind you, that was light, powdery stuff. Heavy stuff takes more effort and a foot of that can be a work out for a trail ride. On her own, she'll just have a blast exploring what the funny white stuff does. :)
Last winter, the snow buried my fences. No problems with my horse getting around.
The only fear with snow is that you can't see what's under it. She is already familiar with her paddock, so no worries.