I'd have a good read into equine nutrition. I wouldn't be inclined to feed horses ANY grain as a general rule & if for some reason I thought it was necessary, I'd only feed it if I could manage little & often meals. There are plenty of healthy, safer alternatives such as alfalfa, beet pulp & rice bran for eg. A good grain free 'ration balancer' or supp should provide the necessary nutritional balance.
While I appreciate it may not be the case with you, show judges often like to see fat horses & award accordingly, so when you say 'OK weight but a little under for your taste', do be aware that many people's 'taste' esp in the show scene because of judge's 'tastes' is unhealthily fat. Obesity & related health issues are epidemic in the horse world, as it is in humans & pet dogs. So you may want to analyse your 'tastes' to be more objective about your horse's weight.
You say the barn feeds reasonable quality hay but you want better. Is it a matter of it being mouldy or such(def not good), or that it's not all rye & clover or such? If the latter, your pony is probably having much healthier hay than those fed on 'top horse hay' which tends to mean ultra rich stuff that can be as good as junk food for many horses.