Gum color in horses is a good indicator of certain health conditions - partly because it's quite, quite easy to look at a horse's gums.
There are two reasons why a horse's gums might look yellow - one serious and one amusing.
The serious reason is liver problems (liver failure is a very common cause of death in older horses) - jaundice in horses often shows up on the gums.
The amusing reason is too many carrots! Alfalfa can also turn a horse's gums slightly yellow. Both foods have a lot of beta carotene, and this can cause a tint of yellow on the gums.