The inclination of many--I'll be quick to raise my hand--is to knock off work if possible between Christmas and New Year's. For an entrepreneur, it might seem to make sense. People have already shopped themselves sick. They've overdosed on more bad versions of the same 23 seasonal songs. So, maybe marketing is a waste of time.
Only, maybe it isn't. For example, if you talk to editors of Web publications, the assumption used to be that traffic would be dead. That has changed. There are a lot of people out and about on the Internet at home during the holidays. Many don't celebrate Christmas and personally see the week as a more normal one. If you don't at least have something planned to catch people's attention, you're missing a great opportunity.
To understand the psychology of people during the holidays, you need only look at your own:
Focusing on overt sales conversion and blatant promotion could seem like overkill after the preceding months of so many businesses chasing year-end consumption. So use a lighter touch. Provide some value other than discounts. Provide information, or maybe just a little entertainment. It's a time for nurturing connections with customers and attracting prospects. (No, a cheesy holiday e-card does not count.)
As others let their efforts slow, yours will also have a greater chance of being noticed on search engines. PR efforts, done well, might also have a good chance because many of those reporters and editors left to hold down the fort may be scratching their heads for story ideas at a time when news is often slow.
Think of it as a small holiday gift for your company.