We used to use studs in snow tires in Michigan up until about 1975 when they were outlawed because lawmakers felt they were causing too much damage to the road surface. Instead, Michigan stepped up the use of road salt which in some people's minds, mine included, causes even more damage to roads from the melt getting into the cracks and sub-surface then re-freezing, over & over, etc., not to mention the damage to vehicles and environment, end of rant. Anyway, studs do increase traction, but when they chew through ice to the pavement underneath, they don't stop chewing. Ice, asphalt, concrete, it all chews up nicely. My garage floor and driveway is proof of this from the studs in my snowmobile tracks.
Here is one of my snowmobile tracks with embedded carbide studs
Here is what happens when trying to load a snowmobile into a trailer if you let the track spin, just a little, when the last few inches are not yet onto the trailer ramp.
This is my driveway, but a different snowmobile.
Studded tractor tires on paved hills, and I would expect a lot of scratched up pavement.
Disappointing thing is that someone could make a decent winter tire for tractors, especially compacts. I was driving back when studded tires were around, I remember having 4 studded Goodyear Suburbanite Polyglas Belted Snow Tires on my 1969 Mustang in the early 70's. I now know that a studless Bridgestone Blizzak is far superior in nearly every test compared to the older studded tires.