The Old Cabin trail can be traversed in both directions, but it's easiest if going from east to west. You can build up some nice speed, but watch out for a short fairly steep section that twists around. The climb out will get the heart pumping.
The climb out in the westward direction is less technical and probably easier. Either way you go on Old Cabin you'll experience a wonderful ride through an amazing area of redwood trees. This trail is a useful route if you want to connector between the western and eastern parts of the park without going to the bottom or all they way up to where Long Meadow and Chinquapin Trail merge together.