Our group does a song we call 'Wassail Round'. I have no idea how old it is, or even where it comes from, but it is very easy.

Here we come a-wassailing among the trees so green.
Here we come a-wandering so early to be seen.
Now is winter time, strangers travel far and near,
And we wish you, send you a happy New Year.

That's it--one verse. The problem is I wouldn't know how to send you the tune. But if you are really desperate, I could try writing the notes and timing down for you. Let me know.

Another good medieval one to sing is "Gaudete", Steeleye Span.