The fan motor stopped turning eye am operating in freezeing temps?

If it's the CPU fan, not long. IF it's the power supply fan, for a long time if the room is cold enough.

Most modern processors are temperature sensitive and have a built in circuit that will shut the computer down until the CPU cools off. Freezing temperatures are hard on devices with moving parts like the hard drive and CD/DVD devices. As a precaution, I would unplug the fan until you get back to normal temperatures. A frozen fan is basically causing a direct short in the fan itself. I would consider blocking at least have the air intake and half the air exhaust to build the temperature back up to where the fan will run, but not totally block them temporarily. This may not make any sense, but at least I would give it a try. Probably not good advice, only suggested. The processor is probably already cold enough without the fan running.