Did medical soldiers really where cloaks or capes like in the books gold cloaks red cloaks?

Yes, although livery tended to take the form of surcoats or tabards or even badges, rather than cloaks. A decent cloak is a good bit of cloth, and since it would be worn primarily to keep the cold or the weather off you on the march rather than on the battlefield, it would be a rather ostentatious display to provide cloaks of cloth-of-gold or proper rose madder to one’s soldiers when homespun wool would do the job as well.