Pressure is pressure. If your regulator is functioning properly, the pressure reading on your regulator is the pressure exerted.
As far as your tank pressure gauge (the one that goes from 0-2000)... that one will drop as temperature goes down. The reason for this is that as temperatures get colder, the density of the gaseous CO2 in the tank lowers, thus lowering pressure. At room temperature, the tank pressure should read about 800-900 psi. In the 30s, it should read somewhere in the 500-600 psi range. There are formulas to calculate these values exactly (I believe it is the ideal gas law "PV=nRT")... but these are general numbers
As far as your regulator gauges, temperature will change the gas density, thus, at colder temperatures, you will have higher concentrations of CO2 given the same pressure. Ultimately, this will change your volumes of CO2 but your pressure should stay at whatever you set it at.
To answer your question, no, temperature should not effect the accuracy of your pressure reading. As for why you have flat beer... (I assume this is what you mean by getting no head) that is a 'whole nother story. It could be from a CO2 leak... the whole soapy water thing doesn't really work with CO2 leaks since that CO2 is coming out at about 500-800 psi... it ain't gonna make no bubbles =P. The best way to test your CO2 system is to pressurize the whole system... say to 30psi, and then shut off the knob on your CO2 tank... if that pressure drops below 30psi within a 10 minutes or so, then you have a significant leak.
If by "no head" you mean "no head but it's still carbonated"... then I'd be lookin' at your recipes or check to make sure you don't have grease all over your glass or something. =P
Clear as mud?