I have a heat pump that work OK in A/C mode. But in the winter, when heat mode is utilized, I have a problem. The unit heats fine but after the room temp is up the blower motor keeps running. This is irritating as the vent is blowing cool air (I suspect ambient air, but it feels cold) on us. Is this a thermostat problem or unit problem?

Based on the product specifications available online, the Noma 043-6131-0 portable air conditioner does not appear to have a heating mode or a heat pump function. It is designed only for cooling and dehumidifying a room.
If you are seeing a heating mode on the unit, it may be a different model or a mislabeled function. In any case, it is always recommended to follow the manufacturer's instructions regarding the use of the exhaust hose. The exhaust hose is necessary for venting the hot air generated by the air conditioning process out of the room, regardless of whether the unit has a heating function or not. Running the unit without the exhaust hose can cause it to work less efficiently and may also create a buildup of heat and humidity in the room.

did you try to set to maximum heat? (suspect the thermostat is defective)

Try setting the thermostat at a normal heat setting. By raising the temperature too high the unit thinks that the heat pump won't be effective and go into strip heat mode.

Why does my heat pump ice up in Winter?
Heat pumps naturally ice-up in the winter. It is normal for the entire coil to be covered in a white frost and even light ice, during cold weather conditions. However, it is bad for the entire unit to be encased in ice. This indicates ductless heat pump problems which should be addressed quickly to save energy and avoid serious damage to your ductless unit. These systems should periodically go into a defrost cycle. This keeps the unit running efficiently. If the coils are blocked by ice, proper heat transfer between the coil and the outside air will not occur.
How does the defrost mode work?
When the mini split heat pump goes into defrost, the reversing valve inside of the outdoor unit is energized, switching the system from heat to the air conditioning mode. The outdoor coil becomes the hot, the indoor coil becomes cold, and both - the outdoor and indoor fans shut off. This allows the outdoor coil to melt accumulated ice. When the built-in micro-computer analyzes that all ice have been melted, the heat pump heating system goes back to heating mode.
A cloud of water vapor may be seen rising over the outdoor unit and a "whoosh" sound can be heard as the refrigerant reverses direction. The entire process usually takes up to 10 minutes (depending on conditions).
How often does the system goes into defrost mode?
Ductless mini-split heat pumps have different ways of determining when to go into defrost. The built-in microcomputer determines outdoor temperature, refrigerant pressures, and several other factors. In colder temperatures the system will go into defrost more often than in warmer.
If a ductless mini split heat pump is severely iced-up in the winter it is possible that it isn't defrosting (though there could be many other causes). Let the manufacturer certified technician check your system

After I have been reading up on your unit it appears that the thermostat is not operating correctly. I found this real basic information on installation for your unit. This link I am giving is pretty basic instal schematics. But seems to be something about your thermostat needs to be dialed in or is not working properly.

http://www.premsales.net/docs/GE/GE%20Minisplits.pdf

I hope this helps some. Mike

Dear Friend!

Due to very low ambient temp, the fan will not run. Once the pressure build up, it's automatically run for some time and again cut off. But if you keep Heat mode and still tem not raised in your room means the reversable valve not working and hence the compressor and out side fan also will not work. Keep "Heat" mode and temp setting +29 to get better heat. Hope is it helpful?

Do not cover!!!!!
A heat pump is a reverse cycle a/c unit and needs airflow!!!!

If it is a heat pump it may not have enough oomph.

Is the compressor running? is the outside unit clean and free from debris? does this unit work in the heating mode during the winter, and is it still capable of that now.

Yes this will recycle the room and can be cover outside if it is not a heat pump and will use elec heat strips to heat. As long as it is tilled toward the back the water will run out the back without a drain kit there should also be a drain hole in the bottom.