I typically just ask if aquarium pets are okay. I only divulge what I have when asked outright. Although, every time I've moved somewhere, I start with..."Are pets okay?" Of course, if there are specifications, I ask about the aquarium pets. I was asked by one leasing agent "Yes, but what do you have?" My reply at the time was simply "A ball python." Her eyes got huge but she said, "Technically, no. But I don't see it, I don't hear it, I don't care." So I think you'll just have to carefully feel them out. (At this point I had become friendly with her, so she was accommodating.)
Dogs and cats typically make it harder than "aquarium" pets do.
I would never stay somewhere that my pets could not go with me, so this is a regular conversation for me. I have moved almost every year since I've been in college. Student housing is awful. lol.