Most cowboys weigh over 200lbs and they ride around on 15h Quarter Horses all day, every day. A short stocky QH with a short strong back and good legs will EASILY be able to carry you.
Not sure what cowboys you're looking at that weigh over 200 lbs. When I quit working cattle i weighed less than 150 lbs. The heaviest rider we had was a lanky 6' 1" cousin who weight about 185. With the exception of Glenn, who's 16 hand QH cross was carrying maybe 220 lbs including his tack, the rest of our QH carried less then 200 lbs including all our tack.
I've never met a heavy person who worked cattle daily (not just sitting on a saddle watching and counting
). With two exceptions, the guys I use to work cattle with still don't weigh near 200 lbs (Glenn does
, but he's tall) and none of us have worked cattle in a very long time. That work will keep you pretty lean.
People who use horses to work cattle try to keep the weight the horse carries down. The horse has to hold up all week and be ready to do it again after a day or two of rest.
Don't know if they still do it, but I've known "Dude Ranches" that place weight limits on riders that are going to ride on their horses for a view days of trekking. That's because it's not the distance you go on a horse that will break it down, it's the weight you put on it.
Most people never experience these effects with their horse and it has less impact, because most are weekend riders. The horse carries a load for a day or two (often for just 4 or 5 hours in a day) and gets the rest of the week off.
But I digress, since this has nothing to do with riding drafts.