My horse is a qhx arab and although not boysterous he has endless energy, will literally just continually go. I can ride out through the hills trotting and cantering for pretty well an hour non stop and he will still want to canter up the last hill... it is just him.
But my last horse was a tb and we (myself, his previous owner and present owner) think he is a rig. He carries on like a stallion around mares, will even try to mount mares with a full erection. He prances around when ever turned out into new herd or if new horse is added to a nabouring paddock. To ride he was the same endless energy but think that had more to do with being a tb than anything else.