1.5 acres of grass fenced in beyond it. The horses are very curious and will come up to us, we're slowly getting more handson time, and are feeding them Purina mini pellets along with wonderful hay grown by our neighbor (we can get this in abundance), and apples from our tree for treats.
As a hoof care practitioner who specialises in rehab, I see more than my fair share of laminitic horses & ponies, so that's where I'm coming from...
The major cause of laminitis is similar to type 2 diabetes in people, and like diabetes, there's not just one 'symptom' - horses generally suffer other health probs besides laminitis from it. When a horse is fat, or in 'good condition' long term, without regular 'hard seasons' to use up fat stores, is when these (natural) metabolic changes take place. So as with people, diet & exercise are important. Horses may also not handle sugar/starch as well as humans & this is also a big factor, especially with modern feeds & 'improved' grasses.
You may find that even that much grass & free choice hay is too much for them. Soaking & draining hay before feeding, to leach out some of the sugars can help, as can turning them out in grazing muzzles part time. These muzzles have a small hole in the bottom & allow horses to eat but tiny amounts at a time. That way, they can have free choice, but not gorge themselves. *Hopefully if well managed, you can avoid their use, at least until the horses are grown though.
Baby horses are far more easily & seriously hurt than mature animals who's bones & joints are 'set' and I wouldn't even be inclined to turn a baby out in a breakaway type halter. Keep that in mind with training too, esp training to tie etc, that just tying a baby up & letting them thrash it out until they accept being trapped is more likely to end in physical damage too. (Aside from, IMO being the totally wrong approach to training)
I don't know what's in Purina mini pellets, but I'd be inclined to be just giving them a good quality, very low dose 'ration balancer' or such, like 'Smart Pak', to give them the nutrients that may be lacking in their grass diet. *Nutrition is a... convoluted subject and I'm no nutritionist, but I do advise you do some homework, because *balanced* nutrition is important & it is not only wasteful but can even be harmful to just feed supps willy nilly or in excess. FeedXL.com is one great resource. Nutrition, as opposed to just diet/calories is also a vital factor in metabolic disorders & laminitis too.
As with people, I don't think occasional or small amounts of 'junk food' is an issue if they're healthy, it's generally 'too much of a good thing' or because they're overly sensitive(often because of 'chronic' diet issues/already 'metabolic'). Remember that minis tend to be naturally more 'sensitive' to sugars than many breeds, and that apples & the likes, while not strictly 'junk food' are full of sugar. So I'd limit things like this to perhaps one a day. Carrots are lower in sugar. But you can always dice them, then you'll have a whole pocketful of training rewards/treats out of one!