When I was at the beach, I occasionally felt the spray of sea water. Is there any word for it?
I think it's called "sea spray."
Are you looking for spindrift ?
Spindrift usually refers to spray, particularly to the spray blown from cresting waves during a gale. This spray, which "drifts" in the direction of the gale, is one of the characteristics of a wind speed of 8 Beaufort and higher at sea. (Wikipedia, "Spindrift")