Some people man... smh

That's when you don't come back the next day. And if she calls you, say: "Oh! I thought you only wanted me for one day!?"

Who thinks that someone is going around losing money training random peoples horses?

Obviously, I'd hope you made it clear to her beforehand what you were going to charge for your services. But either that isn't the case, or she's just a foolish, blatant liar. I find it doubtful that someone could be so asinine as to try weaseling out of paying in this manner, but people never fail to surprise. If it was somehow an honest mistake on her part, she totally deserves it. You have to be pretty naïve to think a professional will render their service free of charge, out of the blue (unless they're a friend, it's part of a promotion, you discuss it beforehand, etc.).

What on earth gave her that impression?

she asked that knowing you're a professional? or did she think you're amateur learning to gain experience? The price should be discussed beforehand if you don't have fixed rates..asking people how they got your number should be part of your business, if the caller has it from a friend, tell them where on your homepage they can find your prices..that way the question doesn't even have to come up..just and idea OP..

Did you not tell her your rates before starting?

This is where my favorite phrase comes in, "Cash up front."

Happens to me too sometimes and honestly is almost always someone trying to get out of paying. I really hope your reply wasn't anything but a variation of "No, it isn't. You owe me x amount of moneys. "

That sucks... training a horse is hard work. Hope you demand her the money she owes you :)