Not every single gun - only the large-caliber siege and garrison guns that made up part of Port Hudson's armament. I worked on Last of the Mohicans as "artillery cordinator" and one day the head of the set design and construction crew asked me if anything had been left out; I told him there was no gun gin. Of course despite his study of period fortifications and artillery, like you he'd given no thought about just HOW those enormous ( and totally anachronistic ) guns would've been hauled around in the wilderness. ( In reality, they wouldn'tve been because cannon that size weren't used in North America! )
A gun gin ( short for engine, like in cotton gin ) is/was a block-and-tackle suspended from a tall tripod and used to mount the tube ( cannon barrel ) onto its carriage. Large siege and garrison pieces were NOT transported any real distance ON their carriages; instead, carriage, wheels, and tube were moved separatly, either dragged or slung under a cart like in this CDV photo, then assembled in place for service. To take it apart is to dismount it, regardless if done by its crew in order to move it to a new location or by enemy counter-battery fire like richard suggests above.
Next time I visited the set, I was happy to see not one but TWO gun gins, a rough-looking one inside the fort and a very nicely-finished one outside in the French trenches!
Edit: JPKH, I misread your original post - you are of course right that when they were originally assembled at the arsenal, each and every tube had to be manhandled onto its carriage, regardless of size; also, when in the field repairs had to be made!