Being a US citizen certainly does not exempt one from local laws, even visiting countries close to home. The OP didn't ask about Mexico, but it serves as a good case in point. From wikipediaWikipedia article on gun politics in Mexico: "The US Department of State warns US citizens [and all persons regardless of citizenship] against taking any firearm or ammunition into Mexico without prior written authorization from the Mexican authorities. Entering Mexico with a firearm, or even a single round of ammunition, carries a penalty of up to five years in prison, even if the firearm or ammunition is taken into the country unintentionally." When I lived in Phoenix, I often read of cases where people inadvertently transporting a few loose rounds of ammo into Mexico wound up in significant legal trouble.
In addition to the penalties for illegally importing or transporting a weapon, you may find yourself on a completely different legal footing. Due process varies from country to country, and even the basic tenet of "innocent until proven guilty" or access to counsel may not apply.