also non trainer, but started lots of my own:
A couple laps is ok at a walk/trot, but I wouldn't do more then that. Keep sessions short and possitive, you want them to have a good oppinion of work when you go to start them. Personaly I don't do much with them as yearlings except showing them the blanket and saddle and getting them well mannered with people. Best to let them be horses as much as possible.
This is the best idea. Do little more than handling them with halter, leading, show them a blanket and saddle, maybe rub them all over their bodies. And give them time to be a horse , prefereably out with a herd. NObody teaches a horse good manners better than a herd of horses.