My shop is nice with an epoxy painted floor so I know what you mean. There are degrees of mud on the floor and while it doesn't bother me, it bothers me. Leaving a tractor out overnight only works sometimes because he humidity rises at night and mud doesn't dry out. Plus, the tire in contact with the ground will never dry so mud sticks there.
Turf tires are the worst at mud, R1's less bad and R4's leave the least mud. I just sweep mud out but after a brewski or two conjure up mental solutions. One would be to leave the shop vac plugged in and near the tractor. When I leave mud, loosely sweep out the chunks and vac up the dust. That's one idea I've thought about but never done.
Another I discovered was to leave sheets just cardboard on the floor where the tires go. Drive on, drive off and easy clean up. You only have to do it when mud is bad. Did this one by accident and it worked well. Old 4'x4' sheets from seed and fert pallets.
That's how I would keep mud out of a shop. Keeping off gravel drive is not possible so I just drive in the grass and find a way into the concrete floor barn. When I have to park in the gravel floor barn the only solution I found was an old HF tarp that I once was too lazy to pick up. It held 100% of the mud when I backed out. Lasted a very long time.
