This is how I worked out the notes and chords of the original movie scene.(Chords below) 
Notice, that it is a Full-Step-down tuning, but Standard tuning sounds just as 
well (If you're playing Chords they would be Am, G, em).
Improvements are welcome!

Far over the misty mountains cold
D------------------------------|
A------------------------------|
F------------------------------|
C-----------0-2-0--------------|
G------0--3-------3-2-0--------|
D--0-3-------------------------|

To dungeons deep and caverns old
D------------------------------|
A------------------------------|
F------------------------------|
C-------------0----------------|
G----0-2-2--3---3-2-0----------|
D--0---------------------------|

We must away ere break of day
D------------------------------|
A------------------------------|
F------------------------------|
C----0---2------0--------------|
G--3---2------2---0-2----------|
D------------------------------|

To find our long forgotten gold
D------------------------------|
A------------------------------|
F------------------------------|
C------------------------------|
G----0-2-3----2h3p2----0-------|
D--0----------------3----------|


The pines were roaring on the height
D------------------------------|
A------------------------------|
F------------------------------|
C---------------0--------------|
G--------0-0--3---3-2---0------|
D--0-0-3--------------3--------|

The winds were moaning in the night
D------------------------------|
A------------------------------|
F------------------------------|
C---------------0---2----------|
G------0-2-2------2------------|
D--0-3-------------------------|

The fire was red, it flaming spread
D------------------------------|
A------------------------------|
F------------------------------|
C----0---2-----0---------------|
G--2---2-----2---0-2-----------|
D------------------------------|

The trees like torches blazed with light
D------------------------------|
A------------------------------|
F------------------------------|
C------------------------------|
G----0-2-3-3---2---0-----------|
D--0-------------3-------------|


Gm           F               Gm
Far over the misty mountains cold
            F                Gm
To dungeons deep and caverns old
         Dm               F
We must away ere break of day
            Gm      Dm     Gm
To find our long forgotten gold

                       F      Gm        
The pines were roaring on the height
               F              Dm  
The winds were moaning in the night
                             F
The fire was red, it flaming spread
               Gm      Dm          Gm
The trees like torches blazed with light