There are openings forward of the rudder pedals, but not for vents. Quite a few areas around the throttles, center console, etc have a panel below them, but don't actually seal the cockpit off from the cargo compt ceiling. There are vents (gaspers) right in front of the pilots, and ducts above their heads for proper heating & cooling. Just the way the plane was built, but not for ventilation. The openings you see do get the plane cold pretty fast in the winter when the visor is up and the wind blows.
The grate in the troop you mention is actually for easy removal to allow for refrigerators to be winched down to the cargo area for replacement. A winch is in the troop overhead (behind the trim panels) to raise and lower fridges. I have not seen that done in that manner for many years. A high reach truck does the job through the troop side door in modern times.
The C-5 ECS does a kick ass job EXCEPT for a very hot or cold troop compartment. It does not have the air volume that the rest of the plane has. So it takes longer to reach the desired temp, but can maintain it ok.