I have not yet gotten the chance to watch the series on TV but I have read the books and without any spoilers from beyond the first book here is the purpose for the tunnel in the wall.

First of all the wall in over 900 ft high that has been built by both man and some magical help. IIRC the tunnel was cut into the wall to create that path to the other side specifically so that they could chop back the forest growth. By chopping back the forest they create a lane of perfect sight to see when someone is attempting to climb the Wall and attack Westeros.

As for climbing down from the top of the wall to the northern side was not something they wished to do as it prevents a speedy return trip.

I have not yet gotten the chance to watch the series on TV but I have read the books and without any spoilers from beyond the first book here is the purpose for the tunnel in the wall.

First of all the wall is over 900 ft high that has been built by both man and some magical help. IIRC the tunnel was cut into the wall to create that path to the other side specifically so that they could chop back the forest growth. By chopping back the forest they create a lane of perfect sight to see when someone is attempting to climb the Wall and attack Westeros.

As for climbing down from the top of the wall to the northern side was not something they wished to do as it prevents a speedy return trip.