It means "It looks like (it's going to) snow." Imagine the speaker looking up at a gray, cloudy sky when the weather is below freezing and saying that. The verb 降りそう is making an observation or prediction about what the speaker believes will happen. そう can be added to other verbs, too, to mean that it looks or feels like (something) will soon happen.

sounds like an avalanche. Snow is coming down (I assume the mountain) I am used to 降る being used for precipitation. I am not japanese though.

Snow is likely to get off