Horses are intelligent although some are undoubtedly more intelligent than others. They have the ability to learn but also the ability to work things out for themselves such as opening stable bolts, freeing themselves from accidents in the field, etc.
A horse is a fast learner with correct and consistent training. Horses will also learn their daily routine and come to know when it is feeding time, or when they can expect treats, etc.
Horses are easily upset but reward training can overcome many problems. Horses make associations with many things and these associations can cause problems - for example if a horse is kicked when mounted a few times it will start to associate being mounted with being kicked and may become reluctant to be mounted. Often problems can be traced to unpleasant experiences and work done to rectify the association. A task or experience which the horse considers unpleasant can be overcome by feeding treats or using something else to give the horse something nice to associate with the unpleasant experience. This can then help to turn the unpleasant experience into a pleasant one. Force and punishment may cause the horse to resent such a task or experience further and so worsen the situation.
Horses can be taught to recognise short words and their meaning but the tone in which commands are given is also important and should remain consistent with the associated word.