Quick Answer:  Fat horses and ponies might look cute but they are at serious risk of laminitis.  You need to restrict the amount of grass they get, at first signs of laminitis you must soak their hay to reduce the sugar.  Can you keep them on a grassless track or a dry lot where they can have some freedom but limited grass and you will likely need a good grazing muzzle.

It is a very good idea to keep a record of your horse's weight as you might be fooled by just looking at them, use a weigh tape and record the figures, we do Skye and Tara every Monday.  Perhaps you can strip graze, if so and you are getting early signs of laminitis like a growing and firm crest - then be mean with the amount you move the fence and yes, soak the hay.

Grazing muzzles are very varied, Skye would not eat with the many different ones I bought, she just looked miserable.  So I invented the LiteBite horse muzzle and she immediately ate with it, due mostly I think to the unique new grazing slot.  It is also soft but strong.

Be vigilant and if your vet or farrier says " he's put on weight "   take notice and take action.