I am cleaning up/ sharpening an old axe that will be used. Should I paint it? If yes, should I prime or just use paint so the paint will ware off during use?
I used a "Red Devil" brush-on enamel on mine. Two coats over bare steel. Allowed to dry for a couple weeks.
Most of the paint stayed on (except for the area immediately around the cutting edge.)
YMMV
The brush hook was painted the same way. It's cleared several miles of trail up at Olympic National Park:
If you want to. I personally prefer to see the metal but I can certainly understand the practice of painting it to protect it from moisture and prevent rust.
That's why the D-ring, bow saw, and loppers are painted yellow.
And yes, the paint will eventually come off any working tool regardless of what sort of paint you use. I found the "Red Devil" stuff to be a bit more durable than simply using a rattle can.
I've painted all my outdoor tools with red paint. Yes it wears off, but only where it is used. Keeps rust down a little. My reason is if there is a debate as to whose equipment it is, the red ones are mine.