A snow golem created on the surface on grass will leave a trail of snow. But a snow golem created underground on stone will not leave a snow trail.
Environment
Swamp Biome. On grass, and underground on stone
MC-47865
Snow Golem won't make snow underground
Resolved
Duplicate
0
Snow golems will not leave trails of snow in a swamp biome - see the wiki for more details on what biomes will work. http://minecraft.gamepedia.com/Snow_Golem#Farming