Temperature is a measure of the average kinetic energy of the air around you. Lower temperature therefore implies lower kinetic energy, which means that air molecules will impart less impulse when impacting a surface. Ergo, less pressure.
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I want to add that by the ideal gas law, pressure and volume are directly related to the amount of the substance and temperature. PV=nRT where P is pressure, V is volume, n is the amount of the substance, R is a constant, and T is temperature. So, as pressure decreases, temperature also decreases to balance the equation assuming that V and n remain constant.
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This is not true in the case of the atmosphere.As per the ideal gas law,the pressure decreases if the temperature decreases provided the volume does not change.In the atmosphere all the three values change simultaneously.That is why the atmospheric pressure is more over the poles,(which is the coldest region on the earth) when compared to that of the equator.As moist air is lighter than dry air and the moisture content is more over the equator,atmospheric pressure becomes less.Another reason for the higher pressure over the poles is the high value of "g" which increases the weight of air and hence the pressure over the poles..