Mud tires just don't do well in packed snow, ice, or even slush.
All Terrain tires, or a combo type tire normally do much better then a straight up mud tire.
Mud tires(MT's) have big chunks of flat rubber for tread. snow and all terrain(AT's) tires have slits in treads that give the tires grip in the snow.
I bought a pair of AT's for winter driving to switch out with my MT's during winter... The difference is big.
But there are some really, really nice combo tires like the Duratracs... but they cost a boatload.
Hope this helps. And like they already said, you can post that question in a different section of this forum and get a lot more answers.