Not permanently. Just like everything else with horses, it takes time to train the hair in a different direction. Worst case, dippity doo hair gel and braiding works. Just make sure the elastics come out easily or you could find your horse rubs a braid (and all the hair out).
Braid your horse’s mane down to the side you want it to lie on. They don’t have to be super neat, and you don’t have to roll them up as if your going to a show, but having the braids in will help keep the mane to one side.