That's really good that you are taking it so slowly with your horse. 2 1/2 years is very young, even for TB's who may race for the Triple Crown as three year olds. Taking it slow and easy now will pay dividends farther down the road.
As far as something to keep your horse interested, I really like trail riding, if you have access to trails. Rides don't have to be long, no rule says that you have to trot at all yet. Getting out of the arena keeps their minds fresh, and the varied terrian can help them build muscle in all the right places. Again, because your horse is so young, you may want to take extra precautions, if you aren't already, with a set of support boots. SMB's are a good name, but I've heard good things about AirBoots and other brands. Depending on your experience with them, polo wraps can be good, but if you choose to go that route, please be sure that you know how to correctly apply them, for the safety of your horse.
Have fun, and best of luck!