Here in Missouri, the winters can get fairly cold.  I store my qr in an unheated garage.  Should I take special precautions as far as running the motor before it has warmed up?  Or is it ok to start it up and drive it with the tyranny cold.  Is it hard on things to rip on a tyranny still cold?

I do not believe you will hurt the transmission running the engine hard when it is cold but you could seize the piston if the cylinder is not warm so the bore diameter has expanded enough  to make room for a hot expanded piston.  The piston temperature almost instantly follows the load and power output of the engine, where the bore diameter closely follows the water temp.

Sometimes the clutch will slip when the oil is cold and thick.