Hi
(NOTE: Two other people replied while I was writing this, so my apologies for any redundancies.)
Depending on how complicated you want to make this, it may not be as difficult as it seems, but I think you will need some time to take in the details.
In Example 4, you get a good break down of how simple or complicated things can be. "Version 1" of that example pretty much uses chords you probably can already handle - Am, G and E, plus F, which you may or may not be doing at this stage but there are ways around it. The melody line is right around the chords in question so it's fairly easy to grasp and understand.
"Version 2" requires some basic understanding of fingerstyle, but again it's all based on the chords you know. In the first full measure, for instance, you form an Am chord, but instead of playing the whole thing, you just play the second and fifth strings simultaneously. To do that, you will strike the open A string with your thumb and then use a finger to pluck (upward) the B string, where your finger is on the first fret.
This discussion of fingerstyle may also be leading to your being confounded about the thumb. Unless I've totally missed something in the text (and anyone here can verify that that is certainly possible as I've done it many a time before!

), any use of the thumb is the thumb that is on your strumming hand, not your fretting hand. You might want to take a look at the "House of the Rising Sun" lesson to help you get started on that.
Anyway, if you can handle the Am, G, E and C chords, you should have a good shot at learning this. Knowing the barre chord version of F is certainly helpful, but there are examples in the lesson (such as Example 7) that help people who are having a hard time with F chords.
Please write more about specific areas of trouble and, hopefully, we can have you playing this for the holidays.
Peace