I have a horse who has not had any experience with anything and I try to pet
her muzzle and she throw her head and looks away.
I think the key word here is pet
. Usually, when I think of petting
, I think of a horse that is free to move into or away from touch. That to me is different from handling
, where we train the horse to stand still and calm and accept our touch for the purposes of grooming, tacking, and directing from the ground and the saddle.
Therefore, what Palomine and Yogiwick were responding to is the OP's expectation that the horse would like to be petted on the head and muzzle. Just from the way the post is worded, I think the OP is new to horses and needs some very basic handling advice.
First, to horses, reaching out and touching their head and muzzle is not pleasant. Only horses who have been handled a lot by people are comfortable with it. Horses approach each other at the withers. To start with your horse, reach toward the withers first to scratch softly and see how he/she responds to that. Don't overdo it. Stop and let the horse move away from your touch or stay there. Move away, looking down or away from the horse after a brief scratching and see if the horse follows you with his eye.
To work on desensitizing the horse to touching the head and muzzle, I would start with the horse on halter and lead and practice the head down cue. Pull down on the lead and keep pulling gently until you feel the horse move its head down. As soon as you feel even the slightest movement (or even the thought of movement) down, release. Wait 5 seconds, then start the process again. As the horse improves, you can increase your expectations (how low, how long) until the horse will keep its head down as low and as long as you want.
From there, you can start the same process with touching different parts of the head, but I find once you can get horse to put its head down on cue, and control the head that way, any other handling of the head just follows very easily.