Mmmm, but it isn't just the Hobbits that experience this. Everyone does. The Rath Dinen is a sacred place, if you respect the dead at any rate. Mordor is the land of the Enemy, and without much life in it except a lot of Orcs.
Everyone is heavily affected by surroundings. Your surrounding affect what you are thinking; what you can do, what you have to do, where you have to go, how comfortable you are, how comfortable you are, what surrounding inspirations you have to think about. The reason this is particularly evident in LotR may be that Hobbits, I believe, take notice of this more deeply than for example Aragorn would, as they are less rough, more jovial down-to-earth people. Aragorn, as well as the other more seriously-minded people in the book, is sterner, tougher and notices these things less, mostly for the other reason that he is in most ways a more cerebral sort of character and therefore less affected. He recognises these 'atmospheres' and surroundings, but is more used to them and does not place such emphasis on them as on his own mind. Other characters are, of course, similar. That is not to say that the Hobbits weren't tough -- of course, they were, although less accustomed to being so as a Ranger would be -- but that they were more down-to-earth and more used to a sheltered, comfortable life, and more involved in what was going on around them.
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