George Patterson wrote:

No, it's not contrary. The "high to low" means a flight from an area of
high pressure to low pressure, not high temperature to low temperature.
When you decreased the temperature, you increased the pressure, which
means you're going from low to high.

Actually Geoerge, it works for temperature as well as pressure.
Going to a colder than standard pressure causes your altimeter
to read high as well.