I find there are usually two responses to this phrase, depending on the frame of mind of the rider who says it. If said pleasantly after a nice ride: I’m going to hack out my horse tomorrow, the listener is most likely to be puzzled, if a bit anxious.
Remember: stand back, and run your phrases carefully through the tin cans and string before you speak in front of non-horse people. Especially if they are ill, elderly, or young and impressionable.
If you say the same thing in frustration after an exceptionally bad ride: I’m going to hack out my horse tomorrow (using your I-could-KILL-him voice), non-horse people will start to ease away from you, trying really hard not to upset you further because they are picturing machetes.
You’re going to HACK your horse?!? Where’s my cell phone? Do I call the police or animal protective services? Everyone will immediately think of the last gruesome newscast where a stunned and blinded neighbor, shielding herself from the camera lights, speaks into the mike shoved in front of her…”You know, he was so quiet and friendly. He was never a bother. I can’t believe he was arrested for murder…how many people did you say?” No one wants to BE that neighbor.
Either explain hacking out before you say it, or use non-horse language: I’m going on an easy ride outside the arena tomorrow and knock around on the trails to give my horse a break.