In a sense, Little Boy and Fat Man—as well as other bombs of the same kind—had parachutes. Not a textile one, but a California Parachute is the name given to the tail assembly
The first nuclear weapon to be used in warfare was the Mk I bomb, also known as “Little Boy.” Delivered by the B-29 Enola Gay, which is now on exhibit at the Smithsonian National Air & Space Museum, it detonated on August 6, 1945, over Hiroshima, Japan, at a height of 1,800 feet. “Little Boy,” a gun-type weapon that detonated by firing one mass of uranium down a cylinder into another mass to create a self-sustaining nuclear reaction, was a result of the Manhattan Project, which started in June 1942. It produced an explosive force equivalent to 20,000 tons of TNT despite weighing just roughly 9,000 pounds.
As the Second World War was concluding, on August 9, 1945, a “Fat Man” bomb was instead dropped over Nagasaki, Japan. The 10,000-pound warhead, dropped by the B-29 Bockscar, exploded over the city at a height of about 1,800 feet. The weapon’s explosive force (yield) was almost equal to the bomb detonated on Hiroshima, at 20,000 tons of TNT. In contrast to Hiroshima, which is very flat, Nagasaki’s damage was somewhat less significant because of its hilly terrain.
When the plan to atom bomb Japan was devised, to allow the B-29s more time to escape the explosions, it was decided to postpone the bombs’ parachute fall.
According to an interesting post on Quora, it can be said that Little Boy and Fat Man, along with other similar bombs, did possess a parachute.
It’s not a textile one, but the California Parachute is the name given to the tail assembly. Inside the square box-shaped fin were shaped vanes that functioned to slow the bomb’s descent speed and stabilize it on a particular trajectory. To guarantee that the bomb had the proper amount of time to be armed, that it was stable, and that the radar altimeters that started the detonators took precise readings, they had to make sure the bomb stopped moving horizontally and was dropping vertically. The bombs’ detonation altitude was critical; the slower they fell, the less the margin of error for the actual detonation altitude.
Thus, the shaped vanes in the tail box retarded both. The angled plates in the tail assembly of the bomb are visible in the photo. These plates served to both slow down and stabilize the bomb by channeling airflow. It functioned as a square airbrake. Tail assemblies on both bombs have been designed similarly.
Photo by U.S. Air Force