Driving saddles generally have trees just like riding saddles. It's very important that the saddle not be placed too far forward. It will affect the movement of the shoulder. I find most drivers that have come from a riding background really want to put the saddle too far forward.
The saddle should sit a solid hand behind the shoulder blade:
The girth should hang straight down from the saddle and be about 4 fingers behind the elbow so it does not affect the movement of the elbow; the elbow needs to move without being knocked by the girth.
The girth need not be tight as well. Especially because driving saddles are not carrying weight like a riding saddle, they do not need to be tightened down. I always say a hand between the barrel and girth is good.
Hope this helps with understanding how saddle placement should be!!