I just sold my '93 'Burb in the spring. Great truck, rock solid reliable and had a strong running 350 with just shy of 250K miles on it.
I used to run HDEO for the flat tappets. Due to the cold winters we see here, I ran Esso XD-3 0W30 HDEO synthetic. I switched at a high mileage with zero consumption or leaks, but my motor was leak free before hand. I am not sure how cold your area is, but a few years ago we saw -40F, although typically -20F is our colder days. If you don't see temps that low, a 5W30 or 5W40 HDEO would be fine. Typically a HDEO 30 weight will be a bit thicker than a conventinal oil 30W.
As for cold weather operation, that old cast iron 350 with a HUGE coooling system (front and rear heat) used to take a long time to heat up. I used a coolant block heater, a winterfront to assist with faster warm ups. I rarely ideled the truck, unless it was very cold. You're temperature gauge is reading low. Check your thermostat and also check your coolant temperature sensor. My sensor went bad a few years ago, and although the engine warmed up fine, the gauge read low all the time. Quick, cheap and easy fix.
I also installed a oil pan heater later on with the truck (I didn't need it, just playing around). In any case, it definitely will make it easier to turn over even with a thin synthetic at extreme cold temperatures. Heated oil will be thinner than non-heated oil. The first number refers to the viscosity of the oil at low temperatures, while the second is the viscosity at operating temperatures. For exmample, 5W30 compared to a 0W40 will be thicker when sitting cold in the oil pan at 0F, but will be thinner when operating at in the engine at operating temperature. An oil (regardless of rating) is always thicker at colder temperatures though, the viscosity rating just measures how thick it is compared to others at the same relative temperatures.