Ground fog is a cool effect, but, as usual, the machines are very expensive, so I tried to build one on my own.
The most powerful modern units are foggers with a strong, mostly nitrogen, cooler afterwards (its fog, not steam).
My first prototype was a copper radiator from my old cpu water cooling system, attached to a pvc pipe and a pond pump for the radiator.
I put the pump in a buckle filled with some freezer packs and water, so I reached nearly 1°C water temperature. Maybe you can get even lower by adding some non freeze fluid. Anyway, the results were way better than expected.
The fog stays on the ground as long as there is no wind or someone walks through. I used HD fluid for this test, but a faster disappering fluid might work even better.