Well obviously to me it sounds like you old horse was over-weight because she had constant access to hay.
My first horse was like that even on pastures with no grain and no hay. She was a pony. The reason I fed her so much hay was too keep her busy through the winter. Believe it or not I do know what Im talking about and it mattered not how much of the hay I fed her because she was cut off from hay for a while because I thought that was making her overweight. No change in 3 weeks so I gave her the hay back.