I hear complaints every year from boat owners who thought the marina would winterize their boat but the marina didn't do it or didn't know it was supposed to.
Disputes arise when the marina and the boat owner don't have a well-defined contract that spells out exactly what's to be done.
The term "winterizing" doesn't have a universal meaning, and your definition of winterizing and theirs may be completely different. Telling someone to winterize the engines and freshwater system doesn't mean they'll also close the seacocks and winterize the head.
If you're hiring someone to winterize your boat, insist on a written contract that clearly lists every job necessary to protect your boat and has a firm time frame, beginning well before the first typical hard freeze. Include language that specifies not to de-winterize until you authorize it in case something comes up and you won't be using the boat through the next winter.
Pay with a credit card if possible. If the boat didn't get winterized properly per the contract and you have damage, you can dispute the charges with your credit card company, which gives you more leverage. Also, don't assume that the marina will routinely inspect your docklines and bilge unless you specifically pay for the service.
Bottom line: Whatever you expect to be done, spell it out in writing.