The woolen cap, known officially as the "Cap, Wool, Knit, M1941" is Radar's signature headgear on M*A*S*H. Known commonly among soldiers as the jeep cap or sometimes as a beanie, the cap was a standard uniform item issued from 1942 onwards to US army enlisted men. It was made of wool with short visor in front and cuffs which could be folded down to cover the ears in cold weather, although Radar would more often wear makeshift earmuffs made from his communications headphones and toilet paper. It was designed to be worn underneath the helmet for added padding and warmth but could also be worn on its own, as Radar always did.
The jeep cap was popular among troops but was apparently disliked by officers who thought it looked slovenly and so from 1943 it was gradually replaced by fatigue caps (such as seen on many of the enlisted men in MASH ). By the time of the Korean War, the jeep cap was no longer standard issue. Nonetheless, it was probably still widely available. Many of the older enlisted men who had fought in World War 2 would probably have one and the resourceful Radar would most likely have been able to trade for it.
Possibly because Radar had made the cap so popular, the US Army apparently brought it back into circulation although modern caps look slightly different from the one worn by him. Jeep caps are also available from commercial manufacturers and used as sports wear.
On M*A*S*H, Radar is almost always seen with his woolen cap. In Season 4 "Change of Command" Potter arrives at the 4077th MASH to find Radar sunbathing without his shirt but with his cap on. In a more hilarious incident, in Season 2 "The Sniper", Radar is trapper with Henry in the shower when a sniper starts shooting at the camp. Radar rushes out to get help. He doesn't take any clothes and just grabs a towel to cover himself, but he does remember to put on his woolen cap! The woolen cap became a symbol of his naivete and youthfulness. In Season 1 "Love Story", Trapper tries to persuade Lieutenant O'Brien to date Radar. He offers to get Radar to shave, clean his glasses or even remove his wool cap.
The jeep cap is also occasionally seen on other MASH personnel especially in those episodes set in winter. Season 1 "Dear Dad" set during the Christmas period, for example, the jeep cap can be seen on both Lieutenants Barbara Bannerman and Becky, and even Klinger.
Season 1, "The Moose", the jeep cap can also been seen on moose Young Hi.