CO2 exists inside the tank as gas and liquid. Basically imagine the tank 80% full of liquid CO2. That liquid will boil off and fill the head-space with CO2 vapor until the pressure rises to a certain equilibrium point. At that point no more liquid will boil off. As you draw CO2 out of the cylinder, more liquid will boil off to replace the gas that was taken out.
Now, cooling the cylinder down changes that equilibrium pressure in which everything stabilizes inside. What this means is rather than that gas in the headspace being at 1000psi, it might only be 500psi. Seeing as how you're regulating it down to ~10psi for serving anyways, it makes zero difference to the performance of your kegs. The total amount of CO2 inside the cylinder remains the same. The total amount of CO2 that you're going to be able to remove from the cylinder for all intents and purposes remains the same. The only thing that will change is you're high-side gauge will read lower. Some people will look at it and say "Hey, the gauge is in the red, you're almost empty" but in reality you're not, they cylinder has just stabilized to a different equilibrium pressure. That's also why high side gauges are more or less useless.
For what it's worth, my gauge has read ~400psi for several YEARS in the fridge.