Megnrose,
You are half right. Cold air is denser. And density/pressure are related. But not the way you are relating them.
Pressure is simply a matter of the weight of the air above you. At surface level, your altimeter will always read correctly if you have the correct QNH set. As you go up, there is less air above you, so the pressure decreases. In "standard" air, it decreases at a "standard" rate.
In cold air, because the air is more dense, it's all squashed into a smaller space. So, as you go up, the weight of the air above you decreases faster than the standard rate - in other words, the pressure is lower than in standard air.
The phrase to remember is "when moving from high to low, watch out below" - that phrase works for both pressure and temperature.
FFF
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PS - A troll is someone who posts messages which are purely intended to cause arguments.