I think it was mainly for conditioning, like running (cardio).
It would be very hard for a Spartan to strength train.
They would need cars and buses.:p
That being said, John's abilities were measured when he first got his augmentations. The Wiki says that a Spartan is supposed to get stronger and faster as time passes.
This is because their bodies adapt to the augmentations.
That would mean that John should be stronger, faster, and have a faster reaction time!:p
Anyways, I think that Spartans only have to do the usual boot camp stuff (Push-ups, sit-ups, etc.) to keep up their health.
Their bodies are supposed to recover very fast from fatigue and their bodies have been modified to pump out more growth hormone, so if John was serious about training, he could increase his strength by tons.
Here's the page. --------->
http://halo.wikia.com/wiki/SPARTAN-II_augmentation_procedures