I think B as cold air will be denser and therefore read as higher pressure=lower height
That's WRONG, and dangerously so. I would strongly advise some reading around the subject before flying IMC in very cold weather. For starters, try ICAO Doc 8168, as I referenced in post #4.
In measuring pressure, the altimeter is actually reading the weight of the column of air
above it. If the temperature is above standard at the altimeter setting source (let's take that as MSL, for example), the column of air from sea level upwards will be expanded compared with ISA ... so at a given altitude there will be more air above the altimeter than in ISA conditions, the altimeter reads a higher pressure and, ergo, under-reads the altitude.
For a temperature below ISA at the altimeter setting source, which is the dangerous case, the column of air is shrunk compared with the ISA column, there is less air above the altimeter, the altimeter reads a lower pressure ... ergo it over-reads.