I have never shown longhorns but i have shown calves at my county fair. to trim the hair between there horns you could just use a comb and scissors, but if your in a hurry use an electric clippers like the ones they cut people hair with.
i don't think you have to cut the hair down their backs unless it's long, but i think longhorns don't have alot of hair on them.

Linda, you are not supposed to trim the hair between their horns or down their backs only the hair around their private areas.