It is a constraint, not a problem, provided you build the trip around it rather than against it.
Plan in half-days. Take the earlier option every time. Expect to lose one activity in three, and choose destinations where the indoor half is worth as much as the outdoor half — which is why hot spring towns, port cities and places with serious food traditions recur so often in these pages.
What genuinely does not work out of season: anything with a single fixed highlight you have travelled specifically to see. If the trip fails without one clear sky, go when the sky is reliable.