Synonyms for Climbable (same or very similar meaning)
WordNet sense 1 (capable of being ascended):
ascendable, ascendibleWordNet sense 2 (capable of being scaled; possible to scale):
scalableWordNet sense 3 (capable of being surmounted):
surmountableWordNet sense 4 (able to be passed or traversed or crossed):
passableFrom the ODE community, based on WordNetadd/edit