I understand that when cooling, an AC unit condenses water vapour from the room, and results in dehumidified or drier air than outside. When in heating mode, I would expect this not to happen, as the cooler coils should be on the outside, so it would be attempting to dehumidify the outside world, not the room. Is this correct (in theory or in practice)?
Yes, that is correct. A closed-loop heat pump work by circulating a refrigerant in a loop, where there are two heat exchangers separated on one side by a compressor and on the other by a valve. Your expectation is correct: In heating mode, the inside heat exchanger does not cause condensation and therefore does not dry out the air.
Having said that, there is one factor to mention. Humidity is often expressed as relative humidity, which is the percentage of water vapor in the air expressed as a percentage of the saturated amount. Raising the temperature of the air inside your house will increase that saturation amount of water vapor. But the actual amount of water vapor in terms of mass is essentially the same, so the net effect is that you lower the relative humidity, even though you don't take any water out of the air. (The dew point stays constant too.)