I am not well versed in Saddleseat, but I suspect most riders in that discipline hold their reins in a manner similar to Trish or the rider on the chestnut. With the exception of Equitation classes where there may be one preferred look, it probably doesn't matter all that much. The main thing is that all the four reins should be neat and show the proper amount of contact. This can be quite difficult in model scale. If you manage to get that part right, I'm not going to worry too much about exactly how those reins are entering your rider doll's hands!
Ok, no more dressage for a while--I promise!