There are a number of similar threads to this one on the site. Probably like oil, you'll get a different answer from each respondent. But here's my take:
Deep lug tires are designed for maximum traction on soft materials, where they can sink in, get a good bite, and push forward like a paddle. The deeper the lug, the more lateral (forward) force that can be applied (provided the lugs sink in to full depth). They have a lot of open space between each "paddle" so they don't plug up with material and become slicks. Great for deep slimy, slippery stuff like mud that wants to flow around the paddle. Chains are like removable deep lugs, but harder and narrower so they apply more downward pressure on the surface.
Turf tires have comparatively shallow lugs, closely spaced. They're more like snowshoes -- they "float" more readily on soft surfaces, but they easily plug up with mud and can't transfer lateral (forward) force as effectively in deep, soft material. Intuition says they don't make good snow tires so why does practical experience show they do?
I think there's 3 factors at play:
1. We're not really trying to drive over the snow, we're trying to clear it down to a solid base underneath -- concrete, pavement or frozen ground. So deep lugs are not an advantage and the shallow lugs of turf tires are sufficient on the cleared path. Things might be different if we were trying to travel cross-country over deep snow rather than clear it.
2. Despite some similarities, snow is not mud. Mud consists of dirt particles, usually rather rounded and coated in water. The surface tension of the water makes the particles readily slip around each other. Snow -- even wet snow -- consists of sharp-edged crystals that interlock with each other. In other words, snow packs more readily than mud. So shallow lugs are more than sufficient to transfer the lateral forces.
3. On ice (or really hard packed snow) lugs can't sink in (although chains will sink in better than rubber lugs). When the tire is floating on top like that, more rubber in contact = better traction. Turf tires have a distinct advantage over widely spaced lugs in this scenario. Just as modern snow tires use narrow slits (called "siping") in the tread blocks to improve ice traction by allowing the rubber to distort and better conform to the surface, turf tires have small tread blocks with narrow grooves to maximize contact area and conform to the terrain.
I could be wrong on some or all details, but I can attest to the fact that turfs work well for snow clearing. Especially if the tires are loaded. And 4 wheel drive makes the biggest difference.