Outside Wall Closet Insulation

[Reese Thompson]

My master bedroom closet on my personal residence is freezing cold!  The closet is on an outside wall, and I think it may not have insulation because the guy who built the home cut a lot of corners.  Does anyone know how to check to see if there is insulation?  I do not have any outlets to pull the covers off.  I also don't have trim to cover up a hole.  

If I were to tear out all of the drywall and insulate it (assuming no insulation after checking), I've thought about lining the closet with cedar.  Would I need to put up drywall again before the cedar, or can I attach the cedar directly to the studs?

Thanks in advance for any help!