It is said that pure breeds of colors white/black/red can't have two-seater skill and only t6+ horses can learn this skill.

Every horse has a coat name and certain amount of color points assigned to it.
So called "pure breeds" are the horses that have color points only in 1 certain color from ones mentioned above.

Breeding horses with enough points in certain colors can warranty/exclude you from getting some foal results - you need to make sure horse parents have enough points in certain color of desired foal (example T8E -pure white - has 8 points white and 0 black/red - so you need to breed horses which have at least 8 points white total).

And until now everything about breeding specyfic horse coats for pure breeds for speed and non pure breeds for possiblity of two seater made sense. Mostly pure breed can be easily spotted just from way it looks :P

But what about dream horses xD?
Arduanatt is pure white - okey, seems logic it wont have two seater, but you can obtain it from any other t8 courser, regardless of coat, just like for Doom or Dine as well.
Doom has two seater - okey, looks like mix of black and red colors. Dine? White and yellow, but not a two seater, hmm ?:o  What color stats have dream horses? Or are they independable from this chart? Then still, why d only doom have two-seater in this case, if Dine doesn't look like pure breed either :P And all t9 horses have their unique skills on side, beside the general t9 skills, so two-seater on doom ain't making it anything more special.

And I d go even more forward and say t10 black/red Arduanatt should have it too, cos is way far from looking pure even if its mythical :D Beside that all time and the effort you need to put in it would be way more rewarded than just floating alone in air xP

Ps. No I don't own t10, I only own fails xD