Pete,

First - I don't really like wearing hats, but I recognize the necessity of having a hat to wear both at work or because of the weather.

The only hats that I carry around are:

Ball caps or hats with attached (chin) strap that I can hang onto a Lanyard Clip that is on my belt.

Touques or Berets that I can tuck under my belt or roll up and put under the epaulets that are on a shirt or jacket.

That's the closest I have come to a solution that will keep me from losing hats.