"Tomorrow is supposed to get snow" is actually correct and sounds like very good English to me. You could also say "It's supposed to snow tomorrow", which is a bit more common.
As 一 mentioned, always use "supposed to". When a verb follows "is/are/am", it usually must be "-ing" or "-ed". "Suppose to" isn't used in this expression. Just remember always use "supposed" in this case.
If you want to know the grammatical reason, literally "to suppose" means "to think" or "to assume." So, when you say "Tomorrow is supposed to snow", you're literally saying "People think tomorrow will have snow" or "Tomorrow is rumored to snow." However, the expression doesn't really mean this anymore; it means "Tomorrow should have snow." If knowing the grammatical reason helps you remember and understand, that's good; but if this is confusing you more, just remember to use "supposed to". :)