I'm the owner of a 22 year old miniature stallion and I've been able to keep him in shape by taking him for walks like a dog. He loves it. Sometimes he trots out ahead of me, sometimes he "heels". I will even go for a jog through the woods where the footing is soft. He pops over little logs. Walking him will not only get him in better shape, but will stimulate him mentally.
I would be cautious about lunging him in a circle if he has a stiff hip.
In terms of feeding, my stallion gets four cups of Sentinel Senior a day and a full flake of hay (because he's a stallion). Obviously it would be different for your guy, but be cautious in how much you cut back if you do. In my 15 years involved with showing minis, I have seen just as much under feeding as over feeding.