It is highly advisable to obedience train your Cairn. Cairns learn very quickly, and the few standard commands can be quickly supplemented with some tricks. Training a Cairn, however, is not like training a Lab or Golden. If you keep the training fun and not repetitive, you both will have a great time. Cairns want you to be alpha, and as such, really strive to please you.
Cairns can be easy to housetrain, mainly due to their desire to please their people.
I strongly recommend using a reward system to house train your Cairn. When the dog produces, be lavish with the praise, and perhaps even give a treat. They keys to this method are that you take the dog out, not just let him out, and all the praise. Your Cairn will quickly learn that going outside gets him a reward, and going in the house gets him nothing. Every person I have spoken with that uses this method faithfully has reported success in a very short time.