What you are referring to is called the 'sagum', and was the prototypical military garment of Rome. It was a generally stereotyped as a red cloak, and serves as a contrast to the white toga (which served as the prototypical civilian garment). Red thus was a colour highly associated with war in Roman writing, and wearing the red cloak within the city was considered highly unusual.

If you're interested in learning more about the sagum:

http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0063%3Aalphabetic+letter%3DS%3Aentry+group%3D1%3Aentry%3Dsagum-cn