A radiator is not necessary for a car to work, specially in a freezing place.
A radiator is needed to refrigerate the engine. In a very cold place the engine is refrigerated just by natural convention. Probably you will have to stop and open the car hood from time to time.
Without globes touching metal could be dangerous, but it is strange. Traveling to very cold places,what you notice is that globes are not accessories, they are vital elements.
Seems like at the very least they could run the engine as long as possible until its about to overheat, then turn it off and it will very quickly return to operable temperatures in the very cold conditions. Certainly better than dying outside in Siberia!
Might still be fine, but... By the time you know it ain't, could easily be too late.
Maybe this plan could work if you drove 2 minutes at a time and kept the hood up. But some of the components in the engine heat up pretty fast.
The truck had a functioning radiator and appropriate coolant levels. The only thing wrong was the thermostat. Even in that configuration, the temperature gauge climbed into the "danger zone" if I neglected the brake-slamming trick.