The reason Fallout 3, and to a slightly lesser extent Fallout 4, are sandy deserts, is because Fallout 1 and 2 took place in sandy deserts, because they were actually in the right part of the world for it.
Bethesda felt the need to maintain the same look for the landscape in fallout 3, even in a region that was once green. Hence all the trees are dead and the land is all dusty rocky sand. Whatever explanations they gave were clearly set up once they'd already decided on the look.
New Vegas had living plants and trees, and as mentioned, snow, because Obsidian apparently didn't feel the need to make it entirely dead, even if it was largely desert.
Bethesda have taken a bit of a step back from the dead everything approach in Fallout 4, where there is at least clean water, scrubby grass and blooming if mutated plant life, so that it feels a bit more like moorland than desert.