I believe that yard work and formalized exercise complement each other.
I lift weights three times a week which helps me when I have big, strenuous projects at the farm, like cutting down trees, moving them to my processing area, separating usable firewood, and organizing. I couldn't manage that if I didn't maintain my strength via weight training. The wood processing is good cross-training -- using slightly different muscles.
Using a push mower has some aerobic training benefit, if you maintain a good pace. I do a lot of cycling to maintain my aerobic capacity but it also substitutes for some car trips. I couldn't do three hours with the mower if I didn't do the cycling to stay in shape.