Without knowing more it's purely conjecture to make such a connection. Carbon steels typically used in engines and transmissions are more than good down to -100C (-150F). Additionally, how do you warm up the oil in a manual transmission other than through conduction, radiation and convection from heat generated from the engine?
With the tranny in neutral and the clutch out the main shaft would stir up the tranny fluid. Some.
With my old Farmall M at extremely low temps I would have to start it in neutral, with the clutch in. Then hold the clutch in for 3-6 minutes before letting the clutch out. Letting out too soon would bog or even stall the engine. After another while I could engage the PTO (which drove the pump for the Farmhand loader) and let that stir for awhile before trying to lift the loader. Since the loader had to be lifted to move the tractor (and I had a dog-food bag strapped across the grill), the engine itself would be plenty warm by then.
I often wouldn't open the barn until I was sure it would start, and then worried it wouldn't start twice, so I ended up sitting in the closed up barn holding the clutch in for the first part, wondering if this would be the time I asphyxiated myself and how stupid my friends would think I was if I did.
My JD 3020 was basically a hydraulic pump on wheels. I installed a destoker so I could start it w/out the starter having to stir the fluid. I'd warm it up a bit and then unscrew that stop screw (which was right next to the fan. I won't tell you whether I was smart enough to do turn the engine off first...)