Can Creepers Climb Ladders?

Creepers can climb up ladders, vines and similar blocks like any other mob, but do not do so intentionally.

Can mobs climb ladders?

Any mob can climb a ladder in the same way a player does: by pushing against it. Mobs are not smart enough to use ladders deliberately — they do not remain on a ladder to get somewhere, but a ladder directly in their path lets them climb up.

Can creepers open gates?

Creepers cannot open doors, they don't have hands. And yes, they can climb ladders, but only if they are directly in the creeper's path of motion.