if you reduce the pressure you also reduce the temp. so as the pressure drops the temp should actually get colder right? Obviously there is not enough pressure drop to see this in action. although last night I was brewing and it was a bit cold out but the propane tank had frost on the sides. This was convenient as it alerted me to the half filled state of the tank.
You are mixing different problems - in your propane tank, the change in temperature is not caused by a change in pressure, it is caused by evaporation of the liquid propane in the tank.
For a closed system like a keg the equation is PV=nRT, where n and R are constants. For a keg V is essentially fixed, so there is no realistic way to change the pressure in a keg other than by changing the temperature.
If it is not a closed system, the equation is PV=nRT where R is a constant. If you change the pressure by venting the keg you are changing n (the amount of gas) and there is no need to vary V or T.
If you change the pressure by CO2 dissolving into beer in the keg then it is not a closed system and you are still changing n. The ideal gas law can only be applied to the headspace of the keg.