No, and neither is wearing heavy armor. It seems like this would come up often enough that it would merit mention in the disabled condition (practically every front-line fighter would encounter this).
However ...
So, if you really felt that bearing a load was strenuous, the rules will support you in your decision.
I'd likely rule that, for anyone encumbered so much that they are limited to 5' steps as full-round action, moving is a strenuous exercise. Of course, given that, they'd need two rounds to move, and the "Begin Full-Round Action" standard action would knock them out in the first round, anyway.