It's best when things like this are spelled out in a lease. For many rentals, the first floor occupant -- the more desireable location -- is responsible for basic care of the grounds. This would be snow removal, lawn mowing and picking up small trash. This is more a custom than a law, and it really needs to be stated somewhere in order to be binding. If this is your landlord, then he may be held responsible by your municipality for providing you with safe access to the rented premises. You should really discuss it with him. Maybe he'll allow you a credit on your rent if you're willing take responsibility for this and relieve him of a problem. At the very least it should be discussed before any further action is considered.