Hmmm, I am on the fence here. I don't think that someone who never has hot drinks should be made or expected to 'share' in the 'drinks round' malarkey. But then again, as a number of posters have stated, the OP's attitude is not great, and she comes across as rather rude, and for someone who is so new in the place, I don't think her attitude (and what she said to her boss) is going to do her any favours.
Maybe an offer to make everyone the first drink of the day - but then no more after that - would be a good idea? Sort of show willing, but not be taken for a ride, making drinks half the day, when you don't have them yourself?
TBH, I have always had hot drinks at work, but only maybe 3 a day (2 in the morning and one in the afternoon,) and some of my colleagues had 2 or 3 times more hot drinks than me, and did expect me to make their (excessive amount of) hot drinks sometimes!
In my office (at the place I worked at for 17 years,) there were 12 people there. Some days there would be 3 or 4 less, (when a few people were at meetings or out for the day/at another office, or off sick or on leave etc,) and it was a massive PITA to have to make 7 to 12 fucking hot drinks. (4 or 5 times a day or more!)
So in some ways, the OP is not being unreasonable. However, I would not have spoken to the manager like that. As I said, she has done herself no favours...