First of all, if they go so far as to open your "ghetto dresser" and look inside, I am pretty sure they are violating your rights. I don't know exactly how it is worded, and it probably varies from state to state, but renters have a right to privacy. Yes, the landlord has a right to come in and inspect the property and do repairs, but they don't have the right to to snooping in your dresser or other belongings.

If they see the animals, or hear noises, or smell odors, then it will become different, sort of like when a police officer has "probable cause" to conduct a search.

So just make sure the animals' enclosures are clean (to avoid odors), and cover them up as has been suggested. A rack could even potentially be turned around so the open side is facing the wall. I would recommend this for any renter, even if there is no clause in their lease, just because of how people can freak out about snakes.