Traditional songs often have really interesting, even tough changes in them. If you are playing them from a chart without any references, keep your tone warm. Just mark out the changes without trying to groove too much.
Most Christmas songs are really familiar and some people are even used to hearing them a cappella, so add what you can to support rather than distract. For songs like these, sometimes familiarity, tradition, and celebration are more important than a sweet groove at the bottom.
This is true except if you're playing songs that are modern versions, like many of the ones on our site. For instance, Born Is the King and He Shall Reign Forevermore allow for a little more groove in the bass line. If you are a bass player looking for a challenge, play Joy to the World by Hillsong, off their new record called The Peace Project. It's a doozy.