I've noticed since winter has started my heat pump is not acting correctly. I have troubleshot the problem and cooling is indeed working fine. Although, when you switch to heating, the outside unit engages but the temperature at the register never rises above room temp. When you set it on Emergency heat, the heating coils engage as they should and it heats fine.

Why is the compressor cooling but not heating?

This is also a single stage outside unit.

It could be the reversing valve or the reversing valve coils.

Is it possible to go about checking the reversing valve?

If you have a wiring diagram for the unit it is possible. Usually I suggest a pro look it over if the homeowner has checked for the obvious.

What brand is the heat pump? With a few exceptions, most heat pump manufacturers use a reversing valve that is powered for cooling. The unit will typically "default" to heating if a problem arises with the reversing valve control circuit. Perhaps your outdoor fan is running but the compressor is not, giving the illusion of a unit running in the cooling mode.

It is also possible the tstat is faulty. It could be energizing the O/B terminals, or not energizing it as needed.

You could also have a busted wire from the tstat to the unit. It all depends on what HP terminals should be energized for heating or cooling.

Let us know what type of unit this is and what tstat you have. Some checking could be done at the tstat eliminate that possibility, if you know how to use a multimeter. Otherwise just call a pro.