We have to guess that Ursula Le Guin really loves Mount Hood. We see it so many times in this novel that it's striking. This isn't a novel about mountaineering, after all.
But Mount Hood's appearance is actually very helpful: it's always there, but its form changes every time George's reality does. That makes it kind of a barometer for how weird the world has become and how reality is changing.
When we begin, we only see Mount Hood as a picture on Dr. Haber's wall:
Dr. William Haber's office did not have a view of Mount Hood. It was an interior Efficiency Suite on the sixty-third floor of Willamette East Tower and didn't have a view of anything. But on one of the windowless walls was a big photographic mural of Mount Hood, and at this Dr. Haber gazed while intercommunicating with his receptionist. (2.1)
So our first glimpse of Mount Hood is a painting on a wall put up by a low-ranking doctor who's trying to have something resembling a view.
That doesn't last long. Mount Hood is the very first thing that we see transformed by George's power: it gets changed into a horse. And that's just the first of its transformations.
Later, when he's become more powerful and famous, Haber gets a beautiful view of Mount Hood through a fancy window instead just of a picture. When the alien invasion begins, Mt. Hood wakes up and spouts fire that burns the surrounding forest. It's not until George stops Dr. Haber's dream that the mountain goes to sleep again.
Again, the mountain is functioning as a measure of what's actually going on in the world. We can tell where we are by keeping track of what's going on with Mount Hood.
Now, one more thing: not all mountains are volcanoes, but sleeping volcanoes are called mountains. Isn't that strange? Isn't it a little weird that we say mountains sleep? Can you see where we're going with this? Yeah, it's probably not a big leap to say that mountains might actually dream… and actually, Mount Hood is associated with dreams several times in the novel.
But which dreams? The ones that go too far, to be specific. Mount Hood wakes up when the aliens invade, for example. Later, when the aliens talk about what happened, they mention that this is the kind of thing that should never have happened. As they put it: "We also have been variously disturbed. Concepts cross in mist. Perception is difficult. Volcanoes emit fire" (9.78). In fact, Mount Hood doesn't go back to sleep until some kind of normalcy is established at the end of the novel.
Mountains should sleep. They shouldn't turn into volcanoes. And some dreams (like Dr. Haber's) should never be dreamed.