I wouldn’t presume to comment whether your horse is too fat based on your photos. I can’t even figure out when ours are too fat.
Round bale vs square bale vs flakes makes no never mind. How large is the flake? And what’s in that hay? Texas hay is probably different from our Washington hay. I remember reading (not only on this forum but also elsewhere on the internet) that some people feed straight alfalfa to their minis. Whoopie!--We were throwing alfalfa flakes over the fence willy-nilly; our three minis were deliriously happy. They loved us! …until our Baby got laminitis. Heart-breaking. Luckily, I don’t think we damaged her.
The vet gave us some suggestions; she told us we didn’t have to do them all (but in between polite remarks about body scores and comments about pasture potatoes) she said we had to do some of them. I chose the easier ones first. We got rid of any bagged feed. It’s loaded with sugars, corn, etc. Ours get free access to salt and a vet-recommended vitamin. I don’t soak the hay anymore; it’s a pain in the butt. However, I do use a slow-feeding net (nibble net) for our two girls sometimes. It slows their eating and keeps them occupied. I hated it, but we also rigged a dry-lot for the girls. And we carved up their (approx) 3 acres of pasture into small sections. They only get limited access; I try to balance their desire to graze with limited access. Our stallion gets about an eighth of an acre, and luckily we didn't have to try to "chunk" up his pasture because he stops eating. He'll save hay for later. Each horse is different.