Radiator Repair in Sub-Freezing Temps

[Fitz]

The overflow nipple broke off the radiator of my 300D, and I need to repair or replace the radiator now.

I bought a new radiator, but that's going to require a complete flush before I install it, and that's going to result in my leaving the car with a drained cooling system or a system filled with water for at least one night in sub-freezing weather if I can't finish in one day.

Would I be safe leaving the system drained overnight or should I wait until I can get the car in a heated garage to start the series of flushes and the radiator replacement?