It make perfect sense, motorcars of the time were mostly open to the environment, and early internal combustion engines had total loss oiling systems. So there

It make perfect sense, motorcars of the time were mostly open to the environment, and early internal combustion engines had total loss oiling systems. So there was always an oil mist dispersing into the air around the running engine and onto the occupants, and eventually on to the ground. Also, there were few paved roads, so dust was a real problem. A scarf or muffler worn loosely around the neck would be raised over the nose to make breathing easier under dusty conditions and to keep oil off the face. My great aunt (RIP) was driving in 1912, I still have her Kansas drivers license, looks like new. After she and my uncle moved to LA in 1913, they both rode their new 1914 Excelsior 1000cc motorcycle all over town.