worst snow storms in us and eu not warming ?, page-45

Yes, my understanding is that high pressure (increasing density) is from cooler air 'sinking' and low pressure (decreasing density) from warmer air 'rising'.

(High and low pressures are relative to the surrounding pressure systems.)

And from the BOM site (I've bolded some for emphasis):

High pressure systems
The air associated with a high pressure system sinks down from above and warms as it does so and is very stable.

A high pressure system (anticyclone), is a system of closed isobars surrounding a region of relatively high pressure. When compared with low pressure systems, highs tend to cover a greater area, move more slowly and have a longer life.

When the high pressure system is located over land the weather will be typically dry and free of cloud.

Where the isobars are elongated around a high pressure system (see Figure 1) they are referred to as a ridge.

Low pressure systems
A low pressure system (cyclone) develops where relatively warm air ascends from the Earth's surface. These are systems of closed isobars surrounding a region of relatively low pressure.

As the rising air cools, clouds will begin to form. The instability of the air will produce quite large vertical development of cumuliform clouds with associated rain showers (such as cumulonimbus cloud).

An elongated extension of isobars away from a low pressure centre is known as a trough of low pressure. This trough usually contains one or more cold fronts.


http://www.bom.gov.au/lam/Students_Teachers/pressure.shtml#high