In addition to checking that the drain in the locker is clear and working have a good , hard look at the locker itself. I just went through this.
V berth cushions soaked. I did not have the higher parts affected though but the anchor locker could account for the cushions.
After emptying all from the anchor locker a close examination revealed fiberglass that held the bottom to the hull sides and bulkhead of the locker but was not water tight. There were pinholes and thin spots. It wasn't going anywhere but it was not waterproof. The bulkhead and the bottom were plywood.
The bulkhead was dry but the bottom was wet I got it dried.
The drain hose was plugged also so the water would pool and find those pinholes.
I opened the drain hole a bit so the drain fitting was recessed so water could not pool at the locker bottom.
I fully fiberglassed, epoxy and Nytex, the bottom and up the sides about 6" paying special attention to the corners with thickened epoxy so the Nytex was held leaving no gaps. Then I applied a final unthickened coat of epoxy over the whole area as a last attempt to seal and provide a smooth surface.
In the process I ensured the drain fitting mounting recess was also epoxied and clothed and the underside of the plywood to farther out than the nut diameter of the through hull used so even if a bit of water gets through it won't be trapped between the through hull and the plywood.
Sounds worse than actual although it was a few hours work.
With your lockers and such getting wetted then of course the windlass, the bow anchor platform, deck cleats and so on should be pulled and resealed.
FF 's suggestion of a hose and towels will help although maybe , depending upon location, you only need wait for the next rainfall.