Mud tires are fine for loose snow, but are worse than summer tires on ice. Real winter tires have tons of siping that really helps grab on the ice. I switch to studded Cooper winter tires every year and will never go back to mud tires in the winter.
They are as good as any all terrain on ice, but yea a winter tire JUST for ice is better. But for a tire that you run all year round, it is great. Run mud terrains year round for the last few years never any issue. Any sledding parking lot the mud terrains are king, had to pull out a few people who wonder why their snow tires ain't helping when they are buried to the diff :d
Even on a packed snow road they do very good, but you have to pick the mud terrain carefully, toyo mt's are a perfect example and are terrible on snow.