As a general rule in the US, a landlord can describe what you can and can not have within the home, mind you, it can be argued that renter’s Insurance or a stiffer deposit could cover this. How ever, once the pets are allowed in the home what is considered “normal wear” changes in the eyes of the law.
Best you ask ahead of time, maybe look more towards houses then apartments, pending if you plan on living here a while, buying is an option.
If it where Canada, there are laws there where the Landlord is very restricted on not allowing pets in the home, Because of what is called Animal therapy, a landlord in Canada would have to prove that the dogs could be a danger to an other tenant… Allergies and that sort of thing would fall in question.
With larger dogs, mainly if they are active, it could be rougher to get in an apartment complex or condo area, but a house should be fairly easy, there are many homes for rent.
THIS will seem way off the wall possibly, but some thing to think about. From the way you write and the words mainly, “expatting” or to expatriate, one would think you are either from England or a British colonized country. Pending on where you are going to live, there will probably be people who would know more about the housing situation.