Any time a horse is tied, there is potential for an accident. Horses are prey animals. When sensing any danger, a horse has a very strong instinct to run. If the horse feels trapped, it may panic more. Some horses have developed a fear of being tied from a past experience of pulling back or injuring themselves.
If you are with a tied horse that is starting to get worried, you may want to untie them. Hold them by the lead rope until you sort out what is causing the concern or the horse calms down.
Always ask about a new horse you are working with before tying it. If they do have a history or lack experience, you will want to know it! Some guardians also may feel strongly about tying (whether or not to do it and how to tie the horse, etc.).
If you tie the horse, be careful not to tie the head too high or too low. Tying too high can strain the horses neck and cause injury if they struggle. Tying too low, or with a slack rope that can droop too low, has the additional risk of allowing the horse to get a foot on or over the lead rope, which in itself could scare him, cause him to pull in surprise and fear, and cause further injury. A horse should be tied so there is enough slack for them to move their head or to rest comfortably, but not so long that they can become entangled or gain momentum if resisting. Be sure the horse is tied to an object that will not break under pressure, which would further endanger the horse or anyone in his/her vicinity. Finally, NEVER tie a horse by a bridle, with a chain over his nose, or with something around his neck, but only by a properly fitting halter and preferably with some form of breakaway clip or tie.