Scarfs and clothing in general are thought of as warmth-bringing but they only reflect our own heat back at us - they're insulating. In Frosty's case the scarf would insulate him from rising external temperatures and keep him cold longer.
I had an old, ratty denim Dickies coat with thick insulation that probably weighed six or seven pounds. I'd throw it over a few water bottles on the floor or the seat, and they'd still be cool when the ones exposed in the backseat were warm, almost hot. Seriously, I had better luck with that coat than I had with coolers without ice.