I've never had snow damage to a shed, but I had one destroyed by hail. My homeowners insurance paid for a new shed and installation.

In all my experience with insurance and "Acts of God" ... insurance WILL pay for natural occurances that are not your fault, i.e., "Acts of God". What they WON'T pay for is damage caused by the policy owner's negligence ... for example, you never clean out your gutters, you let six inches of rust build up in the bottom of your hot water heater, you never repair your sagging fence, your pipes are 50 years old, etc. I guess every policy is different, but I've personally not heard of insurance failing to pay for weather related claims.