How rare is it to find a village in a snow biome in Minecraft?

It is very rare. It isn't supposed to be possible based on how the game code is written. read more

So incredibly rare that it will never happen to you ever, ever. It's impossible for a village to correctly spawn in a snow biome, so its possible to get a very distorted village in snow biomes, but the likelihood to get a whole village undistorted is incredibly, incredibly, incredibly rare. read more

A rare variation of the Ice Plains biome that features large spikes of packed ice, as well as packed ice 'lakes'. Usually the spikes are 10 to 20 blocks tall, but some long, thin spikes can reach over 50 blocks in height. All grass blocks in this biome are replaced with blocks of snow. read more

In some rare cases, villages have generated with a well and nothing else (This appears to occur very frequently on console versions). Upon creation, a village center is defined as the geometric barycenter (i.e. centroid) of the active doors' locations, and the village's size is the greater of 32 blocks or the distance to the furthest door from the center. read more