I agree with KP nut. On our yard alone we have three very different horses all owned by the same couple. One is slim, verging on getting podgy, one is fat, one recovering from lammi is obese. They, up until recently have been kept exactly the same, they share several paddocks and always have access to either grass or hay and have huge buckets of feed too. I still maintain that some horses will get fat on fresh air and others can't eat their way through a mountain of food without problems.
Personally, I am not prepared to risk lammi and I know without a doubt that Belle will just keep eating while there is food available, she was massively overweight when I bought her, she isn't insulin resistant, she had been given Un restricted grass and she just ate and ate, I think the best way to stop horses becoming obese is to have them living as naturally as possible, like Jessey and Jane with Ziggy do. While I agree that horses have evolved to eat almost constantly they didn't evolve on lush over fertilised pasture meant for cows which is predominantly what most of the UKs livery is made up of.