"Would ice build up be a problem ?"
could be .. there are full up heat pumps[cool & heat] available as window units .
as you may know the efficiency of a heat pump in heat mode falls off as the outside temps drop so use on *the coldest days * might not yield full efficiency .when its real cold here[not so very cold] the heat pump wants to switch on its axillary resistance , i have that disabled. in cold damp air they will build up ice on the coils outside
the heat pump senses that someway and heats the outside coil from time to time by reversing its function, quite a sight, at first glance one thinks the unit is on fire so much steam is emitted
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