When Augustus came out on the porch the blue pigs were eating a rattlesnake—not a very big one. (1.1)
This is the opening line to the novel, so of course it's significant. It demonstrates Gus's attitude toward nature: he decides to let it take its course. He doesn't have any interest in imposing his own will on it.
They were people of the horse, not of the town; in that they were more like the Comanches than Call would ever have admitted. (7.94)
The cowboys of the Hat Creek Cattle Company are nomadic, more at home in nature than in buildings. It takes a special kind of man to go on a rough journey like this across the country.
Men who didn't know how to get on and off a horse would not be much use around a cow outfit. (12.119)
Most of the success in a cattle company involves taming animals, and not just cattle. A man has to form a solid relationship with his horse in order to be effective at subduing a few hundred heads of cattle.
Augustus hadn't followed. He was still sitting on old Malaria, back on the little hill, watching the sunset and the cattle herd. (25.48)
It might not be Lonesome Dove itself that Gus misses, but rather the view of the surroundings that the little town offers.
[Lorena] might need to be saved from a flood or a grizzly bear—grizzly bears were often the subject of discussion around the campfire at night. (24.9)
This is a little bit of nature-based foreshadowing. Sure enough, a grizzly bear will show up later, but it's a good thing it doesn't put Lorena in danger. The men learn that nothing can stop a grizzly bear. Some parts of nature are just out of their control.
"Don't get close to them when they got the lightning on their horns. Get away from 'em." (31.29)
Newt learns a few things about the power of nature that he never could have anticipated, like the fact that lighting can gather on a cow's horns. Nature is unpredictable and often dangerous, especially if you don't respect it enough to understand that it's out of your control.
The sight unnerved him so that he shot a snake on reflex—a useless act, to shoot one where there were hundreds. (35.54)
The first death in the book isn't the result of a bullet—it's the result of a snakebite. When poor Sean O'Brien is eaten by water moccasins, the score is Man: 0 Snake: 1. Shooting one snake does nothing to even the score.
"But grass is interesting," [Po Campo] said. "It's like my serape, only it's the earth it covers. It covers everything and one day it will cover me." (47.70)
Po Campo's calmness is rooted in the fact that he is at one with nature. He understands that he's not separate from it; he and the rest of the men are a part of it. So they might as well eat a few grasshoppers while they're there, right? Logical conclusion? Why not?
It struck [Gus] that he had forgotten emptiness such as existed in the country that stretched around him. […] From him to the stars, in all directions, there was only silence and emptiness. (54.21-54.22)
This is what Gus is really searching for in life. Maybe. His relationship with nature is complicated. He is in awe of its beauty here, but this beauty is also lonely. Gus likes being a part of it, but he is sad that it's slowly going away as civilization encroaches.
The grass was wet with dew, so he sat on his saddle blanket watching Dish Boggett point the cattle into the blue distances. (67.48)
This is another beautiful image of nature: the men are like cattle themselves, in a way, simply heading into the distance with no idea what they'll truly find there. That's kind of what we're all like, really, even if we don't realize it. For all our tech and gadgets and all that, we still really don't know why we're here or where we're going.