I divide things up a little more than the previous posters. In a cooler climate, or with light work, a 10W30 HDEO. For an engine in good shape, it offers plenty of protection, marginally better fueI economy and good cold starts. In a warmer climate, or with a lot of continuous hard work resulting in high oil temps, such as towing, a 15W40. Or a tired engine. The harder-to-find missing links between those choices would be a 5W40 HDEO or the new Rotella T-5 10W40, or even the new T-5 10W30 semi-syn.
I had a 6.2L in a Blazer for many years in Colorado and during the winter or on cold mornings, the heavy oil was a serious liability to cold starts if the truck wasn't plugged in. As the previous poster said, they are not all that particular about oil, except (IMO) when it comes to cold starts. MIne needed to spin over well to start well and the heavy oils tended to make that problematic... especially if I was in an inconvenient location (oh, like being camped at the top of a 11,000 foot pass one frigid morning).
Mine had an oil temp gauge and, because of the factory engine oil cooler, I found that the oil usually ran pretty cool, even in hot weather. My criteria for viscosity choice is oil temp, which is related to ambient temp and workload. The oil in mine almost never reached 212F (the viscosity rating point for motor oil). In hot weather (100+F), the normal high oil temp was around 205-210. In the 80s and 90s ambient, a few scratches below 200F Consistent oil temps over 212 would be the indicator that a thicker grade was in order due to the thinning process from heat. Occasional spikes over 212 are no worry, unless they get wildly over and stay there for a long periods. I didn't tow with it, but I four-wheeled a lot in Utah and even on 100+degree days rockcrawling at 1 mph, the oil seldom got overly hot. Transmission... that was another matter!