I would still not tie a horse with any sort of mechanical hackamore or any side pull that squeeze the nose or face with pressure. Their nose could easily be broken by hackamores. Depending on the make and model of it some bitless options are even stronger than a mild bit.I ride with a hackmore bridle so there's no bit so if your horse is well behaved, use one of these bridles. I personally like them better that bits because bits hurt the horses mouth. You can tie them to a post with the reins and it obviously wont hurt their mouth.
Just an aside... the real lesson to take away from this (and remember) is to never be in a rush or take shortcuts when dealing with a horse. When you do, eventually you or the horse will be injured. Safety always comes first.I'm a fairly new rider and just got a really good scolding today for tying my horse up by the reins to quickly go into the shed to retrieve my helmet.