I'm ok with frozen ground and snow but I won't turn mine out if there's a lot of ice either.
It's not a big deal if there's some ice in the hoof "pockets" in the ground, but if the pasture is (or is nearing) the look of a big roller rink, I wouldn't turn them out.
Last year we had a blizzard that put so much ice in my pastures, the horses couldn't even break thru it
I kept the four of them in my one acre flat pasture, that is attached to the barn. My pastures are so hilly, the Co-Op won't come out and spray. We have to do the spraying.
It took five days for the ice to melt in main pastures. That means completely gone off the hills and what was left the horses could easily break thru.
They were really happy to be stuck in one acre, doing nothing but eating hay all day --- no they were not - lol lol
My horses are barefoot. If you have slick shoes on your horse (meaning there's no borium or any type of grip design to the shoe), I might worry on the snow or, if the ground froze into ruts in some places. They could easily get sliding with slick shoes, hit a frozen rut and anything could happen
Hope this helps