It depends of the level of competition and the trial. In professional and high level competitions, white is obligatory for dressage. For jumping or eventing, you can put navy blue, black, cream, brown... But not flashy colors.
For dressage white saddle pad is obligatory. But for cross-country and jumping you can put the color of your choice :) (except neon yellow, green or pink, I guess it won't be very appreciated by the jury!). It also depends of the level of the competition :) most of the time, in club competition there are no rules!