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If this air handler doesn't have electric aux strips in it then the air being produced by a heat pump when it is below 30* outside will feel colder. If the heat pump outside is in a defrost cycle and there are no electric aux strips in the air handler then it will blow cold air while in defrost cycle.
If you do have electric strips then chances are they are not working and when the temperature drops down below freezing outside the heat pump is not producing heat any longer and the electric strips are not coming on to help
It could be the electric strips limits are tripping and when they do they shut down the electric strips until the limit opens again.