Although you get less solar input to the shaded roof during the winter (the sun would be at such a low angle there'd be precious little anyway), the PV panels t

Although you get less solar input to the shaded roof during the winter (the sun would be at such a low angle there'd be precious little anyway), the PV panels themselves put out more efficient power when it is cold out. Almost all solar panels are most efficient in the dead of winter, mostly due to less of a bandgap mismatch between silicon and terrestrial sunlight (note that efficiency and energy generation are entirely different from each other, and often inversely correlate). CIGS, GaAs, and CdTe panels don't have this benefit but they represent a minority of the panels being sold. The argument for putting up shade structures instead of solar panels is pretty spurious- shade structures that last 30 years cost almost as much as PV panels these days, particularly after installation.