The easiest part of a website to change to get into the Christmas spirit is usually the color scheme. Using forest greens and passionate reds will make the Christmas theme obvious. A successful hexadecimal pairing is #085F00 for the green and #FF0000 for the red. If you want a more subtle colors, try #006611 for the green and #993333 for the red. Both of these combinations are web friendly and work especially well when white is the third primary color in the scheme.
For a more sophisticated look, consider going with a "sparkly snow" Christmas color scheme. In such a scheme, the green is replaced with silver and black. The red is still used but sparingly as a highlight instead of as a dominant color. By using silver, black, white and red, a Christmas feel is still achieved while keeping a stylish design. In this look, consider using #EB3216 for the red and #D4D4D4 for the silver.
If you want to avoid bright colors, two alternate ideas are to use a gingerbread theme or a Yule theme. Both of these topics invoke thoughts of the holiday season but they utilize much more subdued colors. For a gingerbread theme, consider a hexadecimal trio of #A45544, #C68160 and #B38671. Web friendly Yule colors include #CC5B10, #7A370A and #F1ED79.
Though you don't need to deck out your website with images of Santa and reindeer, by merely changing the colors, you can get in the holiday spirit while still retaining a professional presence.