Climbing is a skill on RUE 316 which does not mention how fast it is done, unlike Swimming on RUE 317.
A couple frames of reference to enhanced abilities which DO mentions speed...
Climb a spell on RUE 200 allows climbing speed equal to normal speed (ie running).
The Martial Arts Technique "Light Body Climbing" (pg 159 of Mystic China) increases the speed to "half their maximum speed" which is the "ease and speed of walking".