Question:

Noisy compressor is a bad sign, but that noise might be only the clutch……fairly easy to replace for a DIYer.  The clutch gets power thru the low-pressure switch and engages the compressor.  It could also be that a seal has failed somewhere in the system and the gas has evacuated.  No gas=no pressure, no pressure in the system keeps the low-pressure switch open.  Open low-pressure switch means the clutch isn’t getting voltage,  which will keep the compressor from engaging.  I know it’s too late now, but the AC should be cycled for a few minutes each month…..to keep the seals from drying out.  It could also be that it’s just too cold….refridgerant acts different in very cold temps. Your system probably has/had the new R134a refridgerant, but back in the R12 days, it needed air temps above 50