How to prevent snow steps from Snow Golems?

Is there a mod or a command that will stop snow golems from leaving snow on the floor? I made a wonderful home and it's being tarnished by the appearance of the snow!

Solution 1:

After some in-game testing, I have found that Snow Golems do not leave a trail on transparent blocks, including slabs. So you could replace your floor with upside-down slabs to keep the trails off. Adding a carpet will also keep the trails away.

Alternatively, you could light up the floor, but this may not be as practical, since that would require that you place torches on the floor every 2 or 3 blocks. So in this case, your best bet is to go with some transparent block for the floor.

Note: As of Minecraft 1.9 snapshot 15w46a Snow Golems will now no longer leave a trail of snow if the GameRule doMobGriefing is set to false.