Actually, that may NOT be covered!
A hot tub is (for insurance purposes) considered "personal property." Personal property is covered for "named perils" only. (as opposed to your house which is usually covered for "accidental direct physical loss" or "accidental damage.")
Most homeowner's policies have 12 - 14 named perils. The common ones are: Theft, Fire, Wind, Water, etc. So unless your policy names "falling objects" as a named peril. . .Ice falling on personal property would not be a covered loss. Bummer eh? But a hot tub melted by a nearby fire would be a covered loss (damaged by a named peril.)
Now about Wmmcall's tree, that depends! If my own tree falls down because it's dead/rotten = no coverage for damage to my own personal property (hottub or patio furniture. . .named peril only.) But if it hits my house the house is covered (structure is covered for accidental damage, NOT named perils.) If my tree gets knocked down by wind (named peril) both the damaged personal property and structure would be covered. Confused yet?
Finally, if my tree falls down into the neighbor's yard, damage to the neighbors stuff is covered regardless of why it fell. That's because I'm "liable" for the damage (property damage or bodily injury) my tree causes someone else. My neighbor's stuff would be covered by my "liability coverage" which is a separate coverage under any homeowner's policy. Your policy has separate coverage limits for:
Structure coverage: $xxx,xxx
Personal Property: $yyy,yyy
Liability coverage: $zzz,zzz
and different "coverage rules" for each of those categories.
If it all seems just too confusing, remember: 1) Don't try to understand this stuff while drinking! 2) Call your agent, they are trained in this stuff. (In fact, people actually get degrees in insurance. One of the basic ones is called a CPCU.
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we now return you to your regularly scheduled forum (imagine theme from the twilight zone here)