Does snow damage cover pool damages?

It really just depends on your insurance policy and the nature of the damage. Check you homeowners insurance policy declarations page for the term "Other Structures" or "Additional Structures". A...

Besides the mess and cleanup, no.

It depends on each individual insurance - always read the small print!

be more specific - collapse by weight of ice and snow is covered for example......how did the snow damage the roof?

Homeowners insurance covers this. There are many other situations that may occur with trees that may not be at home. Your best bet is to call your insurance provider to be sure.