Crows, like most birds, molt once a year. They don't replace all feathers at the same time, however. That would render them flightless and without protection from the elements while new feathers grew. Molt is accomplished a few feathers at a time.
What time of year do crows molt?
Molting makes birds, including our favorite pair, very cranky. It takes a lot of energy to replace every feather, which crows do in late summer/early fall. (Other birds can molt two times a year, donning breeding plumage in the spring and discarding it in the fall once the kids are raised and out of the nest.)
Do crows molt?
When crows molt, the old feathers can appear brownish or scaly compared to the glossy new feathers.