This is probably a late reply and you know the answer already but I'll reply anyway
You either can buy it in chapter 4 from saint denis stable or you can use the horses glitch in the misson "Horse flesh for dinner" in chapter 3 where you steal 3 horses from the braithwaite manor which will grant you the dark bay turkoman
there is also 2 arabian horses in the misson a black one and a white one choose whatever you like and there is a lot of vids on YT that explains how to get them
