Both Little Boy and Fat Man (and subsequent bombs of that type) did have, in effect, a parachute. Not a textile one; but the tail assembly is called a California Parachute.
The Mk I bomb, nicknamed “Little Boy,” was the first nuclear weapon used in warfare. It was delivered by the B-29 Enola Gay (on display at the Smithsonian National Air & Space Museum), it detonated at an altitude of 1,800 feet over Hiroshima, Japan, on Aug. 6, 1945. The result of the Manhattan Project, begun in June 1942, “Little Boy” was a gun-type weapon, which detonated by firing one mass of uranium down a cylinder into another mass to create a self-sustaining nuclear reaction. Weighing about 9,000 pounds, it produced an explosive force equal to 20,000 tons of TNT.
A “Fat Man” bomb was instead dropped over Nagasaki, Japan, on Aug. 9, 1945, near the end of World War II. Released by the B-29 Bockscar, the 10,000-pound weapon was detonated at an altitude of approximately 1,800 feet over the city. The bomb had an explosive force (yield) of about 20,000 tons of TNT, about the same as the bomb dropped on Hiroshima. Because of Nagasaki’s hilly terrain, however, the damage was somewhat less extensive than of the relatively flat Hiroshima.
When the plan to atom bomb Japan was devised, it was decided to retard the bombs’ descent by parachute, to give the B-29s more time to outrun the blasts.
According to an interesting post appeared on Quora, actually, both Little Boy and Fat Man (and subsequent bombs of that type) did have, in effect, a parachute.
Not a textile one; but the tail assembly is called a California Parachute. The square box shaped fin has shaped vanes inside it; which acted to stabilise the bomb onto a particular trajectory and to retard its speed in dropping. They needed to ensure that the bomb stopped moving horizontally, and was dropping vertically, in order that it had the correct amount of time to be armed, that it was stable, and so that the Radar altimeters that initiated the detonators made accurate readings. The detonation altitude of the bombs was critical; the slower it was falling, the less margin of error in the actual altitude of detonation.
So, both were retarded by the shaped vanes in the tail box. In the picture, you can clearly see the angled plates in the tail Assembly, which both stabilised the bomb, by channelling airflow, and slowed it considerably. It was, effectively, a square airbrake. Both bombs had similarly designed tail assemblies.
Photo credit: U.S. Air Force