Certified GKH Gardening Expert
I would not put too much wood ash directly onto the garden. Small amounts are ok, but too much will "burn" the ground. When wood ash gets wet, it leeches off lye. Lye is caustic and too much will kill the plants. I would add the wood ash to a compost pile to mature it a bit and let the lye mellow a bit.
But, if it is only a few shovels full and spread over a wide area, that will be fine.