It sounds like you have a backwards idea of what's supposed to be happening.
The damper door in the snorkel should rise, blocking off the air path straight through the snorkel (air coming in through the inlet on the bottom of the snorkel, which the flex duct connects to the sheetmetal "stove" surrounding the central collector part of the exhaust manifold, until the engine is good and warm -- then the damper door should gradually lower until the bottom inlet is blocked off and the straight-through inlet is free and clear. This will only occur if everything is in place (air cleaner lid, flex duct, stove), hooked up, and working correctly.
See
here for Chrysler's own explanation.