The biggest difference between the 4/5 speed and the rear axle is the cold weather internal gear movement, and what powers that movement.
With the standard manual trans, cold shifting is human controlled. A person needs to be able to move the shifter from 1st gear to 2nd gear, or from 1st gear into reverse, or from reverse into 1st gear. I can promise you with 80/90 in the 4 speed box, at -20, that becomes pretty complicated. Back in my younger years, diving that 4 speed 66 Coronet in the winter was quite an experience. It sat on the street in front of my house through the winters. The winter of 78/79 was bad, lots of snow, lots of cold. Most nights the over night temps reached a real -20F to -30F, on the nights the temp was higher, we usually got blasted with snow.
When I came home from work, I would park so I could move forward out of the parking place, then I parked the car in 1st gear. In the mornings (5 am) I could shove the clutch in, and start the motor, but I couldn't move the shifter for the trans, there was no put it in neutral to let it warm up. I drove out of the parking space and onto the street. I had 3 stop signs each a block away. By the time I got to the 3rd sign, I could force the shifter into 2nd, and then could shift normally.
The car had a 3:23 Sure grip. Through those first 3 stop signs, the rear was pretty much locked, no sharp turns were going to happen. By that 3rd sign, I could at least make turns. On days the temps were above 0*, the trans shift was stiff, but doable, and the sure grip would at least allow turns if not under power. ATF in the gear box would have been great.
The rear axle is driven by the driveshaft. That motor has a lot more power then a persons arm or the shift rods, levers, and forks inside the gear box. The issue with the gear box is not the gears turning, the motor will easily overpower that, the issue is with gear changing and shifting. With the 80/90 in the rear, the worst thing that could happen would be the differential may drag on turns giving a locked rear feeling if traction on the road surface was questionable. The drive shaft will turn, the gears will mesh, and the wheels will turn (unless there is brake drag). Until the 80/90 gets a little warm, the spider gears may resist moving freely until that 80/90 warms up, so you basically have a sure grip until that happens.
It the gear box never sees cold weather, run thicker lube. If it sees cold weather, run thinner lube. I suspect back in those days with the Coronet, that 80/90 wasn't providing much lube until it got warmed up(maybe that was what warmed up the gear lube in the 1st place). I can assure you, the gear lube wasn't the biggest issue that 4 speed saw, it was the 19 year old lead foot driver.
