[cloudmountain]

I can see that you are really not much of a golfer or you WOULD say "Let's play golf" instead of "Let's go golfing."
Just listen to the announcers at a golf tournament. They NEVER say "golfing" no matter WHAT the grammar books say.

[Fiji Hill]

The only golf I have ever played is miniature golf, and I haven’t gone golfing at a miniature golf course since I was a teenager.

Incidentally, I have heard sports announcers use the term “golfing”—at baseball games, when describing a style of swinging the bat.