We've had fun playing with this song over the years. Take a look at this thread, which goes back to 1997 in Mudcat's early days.
The songs were written in medieval Latin, a language Cicero would barely recognize. I would guess that at the time, most people who could read, could read Latin. Note that the lyrics in the Digital Tradition are from a very poor transcription that appears on the Steeleye Span album. You'll find accurate lyrics in the Oxford Book of Carols, or in the messages in the 1997 thread. There's a MIDI in the other thread, too.
The Wikipedia article on Piae Cantiones is also very interesting.
-Joe, professional Latin tutor-