I can actually think of a way Rock, Paper, Scissors might be done for hooves; Hoof facing upwards is paper, because a flat surface. Hoof facing sideways is scissors, because cutting motions. Hoof facing downwards is rock, because the walking on earth.
*two hours later* Twilight Sparkle: I'm beginning to think this is fruitless. I'm going to have to test this a few more times though to be sure Trixie Lulamoon: The Great and Powerful Trixie shall not accept a draw! If Trixie and Twilight stop now, it is because Twilight accepts defeat!