Have you spoken to your vet about this and how to handle it?
My friend has Paso's....quite a few of them actually.
Most of them are "predisposed" to laminitic issues and being on pasture full-time is a no-no according to her vet.
Best thing you could probably do is limit the amount of food intake by limiting what hours she is allowed to be on the grass. It makes a big difference...
If the horse doesn't need feed, then don't offer it.
It isn't just the sugar, but the carbs, kind of carbs and what those carbs are derived from.
Instead offer a good vitamin/mineral supplement.
Feed only meets daily nutritional needs when fed according to directions....otherwise, don't.
Offer a low-sugar/carb hay in specific amounts not free-choice and yes, a slower feed hay net is a good choice to have the horse able to eat more hours, less food cause there is a finite amount it should eat a day if overweight as yours appears.
Yes, your picture shows a horse in trouble with you saying it is a Paso, there is a look and yours has it!
I'm not in the camp that a horse must eat non-stop...not today with how enriched our foods, grasses and pastures are...
A horse needs to eat to meet their dietary daily needs...how you as the owner fulfill that need is a very different answer and is a specific horse remedy.