The chords in "Jingle Bells" are I, IV, and V; just like a blues. If you play it in C, you simply make C into C7, F into F7, and G into G7. You should also add more a shuffle feel to it and you should be good to go.
For songwriting, Lisa McCormick has a ton of great stuff on the site. Check this out;
The Magic of Chord Theory
Douglas Showalter