What exactly is the teaching of the RCC on the horsemen?
There is no official teaching. Interpretations vary.
White horse is ridden by a king.
He brings the red horse which is bloodshed, the black horse which is famine from the bloodshed and the pale horse which is death and terror.
I think there is a short video about this on youtube done by catholic answers.
However the white horse can signify being ridden by Christ by some.
He that sitteth on the white horse is Christ, going forth to subdue the world by his gospel. The other horses that follow represent the judgments and punishment, that were to fall on the enemies of Christ and his Church: the red horse signifies war; the black horse famine; and the pale horse (which has death for its rider) plagues or pestilence. (Challoner)
I think the latest catechism has the white horse shortening at 5 to 4 on.