That mostly why I carry a shemagh / keffiyeh. It's not waterproof, but it does suit like 50 purposes and is cool in the summer and warm in the winter. It's also light and packs down flat.
You can get them at pretty much any surplus store, or amazon.
I thought they were called tactical scarves. I bought one recently for my husband, and it is super warm. We both use it frequently. Will probably be buying more.
Edit: Just realized I didn't clarify that the term "keffiyeh" is more accurate. I just didn't know it before because of Amazon :)