I bought a used Jeep Cherokee last year. It's a 1998, plain Jane with the 4.0, auto, and 4x4. It came shod with some cheap Chinese tires - I can't even think of the brand name right now, and I've been driving it for 18 months. We've had recent snow and icy roads here. In 4x4 mode, that Jeep has handled what's been thrown at it (snow, ice, mud, water, sand). I'm really impressed what those tires can actually handle. They're certainly not the best, but they haven't let me down yet.
That being said, after looking at several reviews, my next set will be some General Grabbers.
My problem has always been driving through the creek, then the silt that gets deposited on this side and then the mud wallow at the end of the pasture closest to the house. My favorite has been the Kelly Safari AWR mud tires. I don’t think KelIy makes them now. If they’ll shed mud and not turn into slicks, they’ll do the same with snow. I always got decent life out of the Kellys.
They do make noise going down the road.