Just a point of order from someone who used to work in hotels: Birthday's aren't unique. About 20 million people share your birthday. Additionally, taking a trip to celebrate a birthday isn't unusual. As such, there will probably be multiple rooms with a birthday guest on a given weekend.
As for-profit businesses, most hotels avoid giving away free stuff to anyone celebrating a birthday, anniversary, graduation, or other event. In the hotels in which I worked, we only did it for frequent guests of our hotel.
Please note that I'm not saying this to be mean. Rather, I'm simply trying to moderate expectations about receiving a free gift from a hotel you've never visited.