Oh, 3 salons...not likely to be an error, then...
While he did not use the word 'gift', saying 'I have booked you in for A, B, C' certainly implies that it's on him.
I think honesty is the best policy in this case. It is embarrassing but if he thinks this is acceptable then he needs re-educating!
I would straight out tell him that you are embarrassed to have to raise the matter but that when he told you he had booked you in for treatments (without being asked to) you naturally assumed that it was his treat and would be picking up the tab. Explain to him that it was embarrassing at the first salon because you assumed there had been some kind of oversight on their part...until the same thing happened at the next two salons. Also explain - since you believed it was a gift from him - that you may not have taken your purse and could have been in the very humiliating position of not being able to pay at the first salon, and on that basis, cancel the next two appts.
Did he buy you a Christmas present? If so, he might have thought it was a foregone conclusion that he was basically making sure you committed to a little 'me time' while he looked after your DD but would not be paying? Still, he could have made sure you understood the gift was the gift of time to yourself and you'd be paying out of the money you have for family spends? I would have expected him to make that clear, or at least, given me the choice of what kind of 'me time' I'd like if I was paying myself...
In your shoes, I would have fully expected not to be paying and would be bewildered and a bit miffed tbh. And, I would have to let him know my feelings if I were you.
Unless you know he a joker...in which case, he may in a few days spring it on you that it was a joke and hand over the cash?
I wouldn't be able to last that long but it would strengthen your position if you did this as you can say that you were so sure it was a joke and he was going to come clean and reimburse you that you hadn't brought it up - that sort of reinforces how unacceptable you think it is!