"No, you don't say?!"

Seriously though... There is an ini setting in skyrimprefs.ini that says "bEnableTreeAnimations=1". Shouldn't that cause some wind effect at least? The grass is moving in the wind but the trees are completely still.

You'll have to use a mod if you want some better wind effects on trees. Although, there should be some subtle movements by default. Delete your ini file and let the game regenerate a new one and see if that fixes it.
http://www.nexusmods.com/skyrim/mods/32723/?

Yes, should be...lol

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Check this too:

SkyrimPrefs.ini -> Display section

fTreesMidLODSwitchDist

Is this set to 0 (zero) ???

Trees were not moving in my game either until I bought a new computer, with a better, and more recent, hardware.

lol

No, it was set to 5000 but changing it to 0 didn't do anything. I'll check out that mod and see what it does.

EDIT: Actually I don't think I have the hardware for it. My FPS are only between 15 and 25 outdoors most of the time, and this mod requires 30+.

This is a misunderstanding, i guess. (Probably my mistake)

It shouldn't be zero. !!!

It should have a value. So yours is 5000. Do you see any difference if you raise it up to 12000 ???

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However, as your PC is a little weak, just leave it as it is.

I'd only start to worry if they came to Dunsinane castle.