There’s no difference, that’s usually the same horses but the qualities required for a good horse one ice are different. On grass, we prefer a handy horse because the field is big, the ball is smaller than the snow ball.
On ice, that’s more physical than on grass, the field is smaller, the efforts are more intense, the markings are more frequently. On ice, that’s most of the time the less good ones on grass who are the best because the game doesn’t stop, the horses are slowed because of the snow so the speed is less important. The most important on ice is the power.