The Mangalarga Marchador horse can have one of three different gaits and be correct: the marcha picada
, a lateral gait similar to a stepping pace; the marcha batida
, a diagonal gait similar to a foxtrot; and the marcha de centro
, similar to the running walk of a 1930s era Walker. I've got all three gaits in my herd; all will back up on command without difficulty. It was no more difficult to train one than another.
IMO it's a myth that the laterally gaited horse has more difficulty backing than a diagonally gaited horse. It's all in the skill of the person teaching the manuever.
This is not to say, however, that all horses are equally easy to train to this manuever; they are not!!!
Rather, any training difficulty in my experience is unrelated to the gait being performed.