Known by the nickname "Hot Henry", Barber was an advocate of clean climbing, a prolific first ascenscionist and free soloist.

His repertoire of moves, creativity, and problem-solving abilities, and his tremendous self-confidence and mental control, set him apart from his contemporaries.

[1] In 1976 Henry (with Steve Wunsch and Fritz Wiessner) traveled to Dresden, East Germany as the first American climbing visitors.

Tradition (and soft, fragile sandstone) demanded that rock climbers use no metal for protection, relying instead only on knotted nylon slings jammed into cracks to hold a leader's fall.

[2] In early 1978, Henry and partner Rob Taylor attempted the first ascent of the Breach Wall on Mount Kilimanjaro in Tanzania.

After he recovered, Taylor wrote articles and a book (The Breach, Putnam, 1981) painting Barber in a very unflattering light.

Barber continued to climb at a very high level after the Taylor incident, for example making the first free ascent of Women in Love (5.12), Cathedral Ledge, New Hampshire.

He eschews modern camming devices and harnesses, preferring the simpler, more rigorous style of nuts and swami belt.