I usually carry a disposable medical face mask in a baggie along with some tissues and my asthma inhaler. It's the type with elastic straps that hook over the ears. Good enough for our occasional cold dry days that aggravate my asthma. Adds just enough moisture and dust resistance to help, and doesn't get soggy from my breath or sweat. No worries about cleanup, I just toss and replace 'em after use.

Disposable medical/surgical masks are available with designs too, if you don't want to look like a rolling surgeon or patient.