Minecraft wiki entry for Time-saving_tips, associated text: Snow golems do not leave snow trails in plains, swamps, deserts, beaches, jungles, mushroom islands, or the Nether. In deserts, jungles and the Nether, they also rapidly take damage and are very hard to keep alive. If you're stuck in a bad biome but are near a river or ocean, try to build a platform over the water.
There is a trick that allows you to leave the mouse clicked while snow generates. This, however, will break shovels quickly (a gold shovel breaks almost instantly, and a diamond one breaks in roughly two minutes).