As I understand U.S. export regulations, a barrel is a reestricted part and requires an export license, and Canada requires an import license.
I would assume that while buying a restricted part in the U.S. would probably not be a problem, shipping or taking it into Canada without those licenses would be illegal.
If you have a copy of the Gun Parts Corp. catalog, they have a list of restricted parts and an explanation of their export policy under Ordering Instructions. The give a web site address for further infomation:
Actually Canada doesn't require an import license but will provide one since the USA requires one to provide an export license.
I live less than 30 minutes from the US border and travel there almost weekly.
I wouldn't do anything to jepordise my clean record.