Do barbarians get uncanny dodge? not according to the manual, only rogues get it according to the manuall, but i'll check in game. But anyways since it doesn't say that you must wear light armor I would assume that it would work with any armor.
light armor = leather, studded leather, hide armor. Might be more just right click on the armor and look, it will say what armor it is.
unfortunately i think you cant use the uncanny dodge ability wile wearing armours that arent light
no man is truly free exept the mentaly unstable for only he can jump of a cliff fully convinced that he can fly ...
unfortunately there is also gravity
Clarifications
Yes Barbs do get uncanny dodge
Leather and Studded Leather armors are light, Hide is medium
and no you don't have to wear light armor to take advantage of Uncanny Dodge.
It is best to be thought a fool and stay silent, than to open your mouth and remove all doubt.