You are NOT being paranoid.
A compressor can be damaged or destroyed when operated in cold temperatures.
Most manufacturers will have a blurb in the manuals about 55 or 60 degrees.

One other thing that is missed by HI's (as far as I can tell) is the prohibition of starting a compressor if power has not been on to the condensing unit for 12 hours or so.
Both conditions can cause "slugging" where liquid refrigerant migrates to the cold compressor and is sucked into the intake valves and cylinder(s) of the compressor.
Liquid does not compress very well, tends to break pistons, rods, and discharge valves.

Since I have a background in A/C, I tend to push the envelope, but I would not recommend it.

It is just like if there is snow on the roof, or the power is off, you can't inspected what you can't inspect.
BTW, an A/C tech can't operate it when it is cold either.

__________________
Jim Luttrall
Mr. Inspector.net, Inc.
Allen, Texas 75002