Horses should have a quick basic grooming on a daily basis.  Curry the coat first to raise up the dirt, dried mud, and loose hair.  Don't curry over "boney" parts like the spine and the lower legs; that hurts!  Then brush off the excess with a Dandy brush - that will bring up the natural shine.  Gently separate hair in the mane and tail and then comb through with a mane comb.  Never use a human brush or fight with the snarls!  That will just pull out the hair and thin the mane and tail.  Gently brush the face with a face brush; most dandy brushes are too large for this.  Finally, use a hoof pick to clean out the feet. 

On an occasional  basis you should bathe and condition your horse coat with a good quality horse shampoo.  Doing this too often can dry out the coat, so don't over-do!  Use a scraper after you shampoo to remove the excess water. A good conditioner/detangler like Mane and Tail will make it easier to comb out the mane and tail without pulling out hairs.  A spray shine product can add some luster, but be careful not to spray the saddle area.  You may find your saddle slipping!  Remember, a truly shiny coat comes from a healthy horse, not a spray bottle.  

If you are going to be showing your horse, then make sure that you have braiding tools and fresh, new yarn. If braiding is new to you, then start practicing now and invest in a good video or how-to book. Practice will definitely make perfect!