I already searched for this, with little success:
I needed a clever way to get snow, but it appears snow golems don't leave snow in ANY biome. Just leaving it here, and attached image of snow golem in snow biome, not leaving snow.
On another note, how many times is it possible to mention snow in a sentence?*
Too many
Duplicate of MC-377 – If you have not, please use the search function in the future, to see if your bug has already been submitted.
I have tried this, and it seems that your issue stems from having mob griefing disabled.