Mine can go straight sideways REALLY fast..... when the kangaroos decide to hang out next to the arena haha!
I suspect that's more of a side pass is it not?? We don't do directly sideways as such in Dressage - unless you're riding a nut job! Though, I do sometimes ride direct sideways as an exercise when my horse is feeling a bit sticky to the lateral aids.
Down the long side of the arena, then ride a 1/2 pirouette, then straight across the arena and same on the other rein.
Certainly makes your trot work more uphill!!!!
Haha no nut job, but it's funny you say you do it when your horse feels sticky. I do it too.....I push him sideways, but he must be soft, then I do a half turn (haha half pirouette) then go the other way.....it's sooo funny that we are pretty much in two different worlds, geographically and discipline wise and we practice the same things.....guess there more than one way to skin a cat!!!
Of....my half turn is more of a slow roll back....