I have medical reasons to need a fridge in my room for medications.
I have had, with few exceptions, all of the rooms that I stayed in that did not have a fridge comp the fridge when it had to be placed in the room at the IGH hotels in their chain. I also had Fairmont Hotels, Best Western, and many others comp the fridge also.
For that kind of room reservation when I am booking I will put a note under the special request " Refrigerator for medical reasons".
I will then call the hotel in the morning before I check in to confirm that a fridge will be in my room.
I ask if there will be a charge. If I am told there will be, I remind them it is for medical reasons. If I am still being charged, I will ask to talk to a manager and this usually quickly resolves it and I am not charged.
I must mention that am in the IHG Rewards Club, have Platinum Elite status and have been for many years, so I do believe that helps with this issue in their chain. I am also a member of quite a few other programs.
I would recommend joining the loyalty program of the chains you stay so that a hotel staff member or manager can see in their computer that you are a loyalty member when they look up your reservation and check in.
I would call the hotel ahead of time to arrange the fridge, just the way you would confirm the details of a reservation. In some hotels there are only a few fridges, so I would make sure you explain it's for medical reasons so that they have one set aside for your needs.
Politely letting the hotel know what you need and why.
Perhaps you could call and check on a hotel's fridge in the room policy prior to making a reservation. Also make a few calls to see if other hotels in the area you need to be would consider comping the fridge based on your need before you book so there are no misunderstandings.
I don't think making ADA demands for a blanket " no charge" request to their corporate offices is a good idea.
With the ADA for most things, if the accommodation legally has to be made, the person requesting it still has to pay for the accommodation or modification, such as is the case of rental housing and shower bars being affixed to the wall.
Hotels and their staff will be very happy to be helpful, they just need to know what you need and have enough time to accommodate the request.