You really don't need any 'special' products. Feed the horse appropriately and it will have a good skin and coat. Keep it clean as a matter of course, instead trying to get it clean the day before a show.
Use a drop of white vinegar in hot water and hot cloth the grease out of the coat. A few drops of baby oil will keep the tail tangle free.
If you showing at championship level and under lights, pig oil used sparingly will enhance the topline.
I was very frivolous the other week and bought some 'glistening oil' it is rubbish and just attracts the dirt - awful stuff - yet I know some people just us it all the time. I usually don't use anything.