I have used Mobil 1 synthetic engine oil(5-30) in my unheated air compressors for near 20 years with no problems starting at 30 below 0 temps.
Engine oil has water dispersant additives that mix condensation water with the oil and depend on hot pistons to boil off the water. An air compressor may not run hot enough to boil off that water, but has not been a problem in my units. Might be a problem in areas with very high humidity, but I have not seen it. I change the oil once per year, and it comes out looking nearly new.