Horse driving commands vary a lot from place to place, so can't be sure.
However, the most usual words in the UK (and no doubt elsewhere), are gee or gee up for go forward, whoa for stop, ree for right and haw, hey or heck for left. Right can also be "come round" and left "get over" (but I may have that backwards). Back is usually "back"...
A really good draught horseman is supposed to be able to back a cart into a shed by voice alone.
My own cob does not yet know left and right, but knows "trot" so well I have to be careful not to use the word by accident, or I'm off down the road before I know it.