Wear a big scarf ... for guys or girls ... a scarf comes in handy for all kinds of emergencies including using it as something to cover your mouth, dress a wound, tie something or cover something up.

Everyone should look up what a shemagh is, and all multitude of uses it has. Pretty sure there are plenty of colors that aren't tacticool, which is inevitable when you search for it. If it works for the grunts the US sent to the Middle East, and actual Middle Eastern cultures, it'll work for you. Hitchhikers' Guide to the Galaxy describes how useful it is to carry a towel across the galaxy; this is it.

Edit: something more that I recalled of when I was in the prepper phase years ago: Marines swear on this thing called a woobie. It's their safety blanket, figuratively and practically. It's basically a quilted fabric liner under a poncho for insulation. Works just as well as blankets if you're going to be crashing somewhere overnight.