Jim Anderson wears a hat a lot, but I do not remember Ward wearing one. Maybe in the episode where he goes out of town and leaves Wally in charge, but I am not sure.

Good Point
Men's Hats were THE thing for like 50 plus years / even more, and then Ward shows up without one !

Quite a progressive image for it's time !

Like Mary Tyler Moore in slacks on Dick Van Dyke Show ...

In the accordion episode he's admiring himself in the mirror, wearing a hat.

I also remember him wearing the hat when he's getting ready to go out of town.

In one thread I mentioned 4 episodes and what they had in common.

Beaver’s Accordion
Garage Door Painters in the beginning
Substitute Father
Happy Weekend

Ward had a hat on.