The Am chord in the verse is a finger-picking part:
E|-------------------------------|
B|-----1---------------1---------|
G|---------2--------------2------|
D|-------------2-------------2---|
A|--0----------------0-----------|
E|-------------------------------|

The * signals to move your 2nd finger:
E|----------------------------------------|
B|-----1------------1------------1--------|
G|--------2------------2------------2-----|
D|-----------2------------2------------0--|
A|--0------------0-------------2----------|
E|----------------------------------------|

The C chord following the Am has the same picking-pattern.

The D-G chord picking pattern is as follows:
E|-----2------------------3-------------|
B|----------3------------------3--------|
G|---------------2------------------2---|
D|-0-------------------0----------------|
A|--------------------------------------|
E|--------------------------------------|

Then strumming resumes with the G chord.

The Am chord in the chorus is not finger-picking, it's strumming.

This Am chord still requires moving the 2nd finger.



[Intro]

G     Am7      G      Am7 


[Verse]

Bm        G       Bm         G
Childhood living  is easy to do
Am               *   C     D G                    D   Dsus4 D  D Dsus2
The things that  you wanted    I bought them  for you
Bm        G    Bm             G
Graceless lady you know who I am
Am          *   C     D G                    D   Dsus4 D Dsus2 D
You know I can't let you  slide through my hands


[Chorus]

Am * C    D  G         F       C
Wild horses   couldn't drag me away
Am * C    D  G         F       C
Wild horses   couldn't drag me away


[Verse]

Bm            G      Bm            G
I watched you suffer a dull aching pain
Am   *      C     D G              D   Dsus4 D Dsus2
Now you've decided  to show me the same
Bm          G     Bm            G
No sweeping exits or offstage lines
Am          *    C     D  G               D  Dsus4 D Dsus2 D
Can make me feel bitter   or treat you unkind


[Chorus]

Am * C    D  G         F       C
Wild horses   couldn't drag me away
Am      * C    D   G        F        C
Wild wild horses    couldn't drag me away


Fmaj7  Cmaj7  Fmaj7  Cmaj7  C D  G


[Verse]

Bm             G      Bm            G
Faith has been broken tears must be cried
Am       *    C     D G           D   Dsus4 D Dsus2 D
Let's do some living     after we die


[Chorus]

Am * C    D  G         F       C
Wild horses   couldn't drag me away
Am      * C    D   G        F        C
Wild wild horses    couldn't drag me away

Am      * C    D   G      F        C
Wild wild horses   we'll ride them someday
Am      * C    D   G      F        C
Wild wild horses   we'll ride them someday