Ascots (they were known simply as scarves at the time) were not a regulation uniform item during World War II and seem to have appeared in the European Theater only very late in the war (spring 1945). I have seen images of general officers and airborne enlisted troops wearing scarves, but there doesn’t appear to be a pattern of issue or wear for this uniform item.
The scarf became a more widely-issued uniform item a few years later during the Korean War where they seemed to become more of a ceremonial uniform accouterment seen at formal parade formations and award presentations. These scarves were generally made of rayon and were seen in the wearer’s branch of service color (infantry-light blue; cavalry-yellow; artillery-red; etc.).
I hope you find this information useful.