As Anna says, it really depends on what your lease says.
I'm not a lawyer, so what follows is not legal advice. For that, you need a lawyer. However . . .
if your lease doesn't address the utility trailer one way or another, it's still likely that your lease has some sort of language about the owner having permission to visit or inspect the premises with reasonable notice--such as 24 hours' notice . . . except in the case of an emergency in which no notice is required. Again, read the lease. But if it has language like that, then the question, from a legal standpoint, is whether that permission covers only the physical house, or whether it covers the entire property (which would include the trailer). I don't know the answer to that. But if the landlord is required to give 24 hours' notice before stepping foot on the property, you'd have some protection. On the other hand, the landlord could notify you daily that he planned on visiting the trailer in 25 hours.
And I doubt there's any restriction in your lease forbidding him from keeping a trailer on the premises. But, again, read your lease.
As a practical matter, the best thing to do is to talk to him and try to work out some reasonable accommodation.