Basically I would make the ladder an actor, set the collision to type sensor, set it to cannot move, and make a separate collision group for ladders which only the player can collide with.
Then for the player you need a behaviour. This shouldn't be so different from wall climbing:
If the player is colliding with a ladder and he is not jumping:
- If he is not climbing, check if up or down key was pressed. If it was, set "he is climbing" and prevent falling.
- If he is climbing set x speed and y speed to zero, then if any of the arrow keys are down set x-speed and y-speed to a fixed amount depending on which keys are down.
If he is jumping you should set "is climbing" to false.
There might be some things to add for when the player falls off the ladder, or he collides with a wall, (if you use wall sliding/jumping) when the ladder is next to a wall. It will also be easier to have a separate jump key and climb key, especially if the character is supposed to be able to jump from the ladder. I don't have too much time now, and I don't think I can think this through without doing it, there might be depencies in other movement behaviours. But you should try it out and then post what you got.
-- Edit:
You might want to put what i wrote outside the collision behaviour. In the colliding with ladder-group behaviour, only set an attribute "collided with ladder" to true, then in a "when updating" behaviour you unset collided at the end. Otherwise there would be no way of unsetting collided, as the collision block would never be called.