These days, Christmas in Croatia is much like many other countries that celebrate this holiday - there's a multitude of decorations, fir trees aplenty, a slightly manic shopping period for gifts and (more or less) a good holiday spirit.
Almost all towns and cities decorate their centres and main squares with the usual kind of Christmas decorations (think plenty of lights!) and put up a large Christmas tree.
As a small aside - one Croatian family has really taken Christmas decoration to heart! In the small village of Grabovica, east of Zagreb, each year they decorate their property (buildings and land) with an amazing amount of lights, normally bettering themselves each year! For Christmas 2011, they plan on using 1.2 million lights. Here's a little video of the end result from Christmas 2010:
Many places often have some kind of Christmas fair, with stalls selling food and drink (mulled/hot wine!), Christmas ornaments and other little trinkets. For example, for Christmas 2011, Dubrovnik is having two such fairs (in the Luza and on Gundulic Square). These fairs normally start in the first week of December, and go through to early January.
The larger towns and cities will also have an ice rink. Most weekdays, time is alloted for schoolchildren to skate (or learn to skate!) with open skating for all taking place later in the day. These stay open well into New Year.
New Year's Eve is also very popular in Croatia and, once again, many towns and cities organise a special celebration for their main square or street. In the larger cities, this can often be quite an extravanganza with top singers (by Croatian standards, anyway) performing. As in almost everywhere around the world, there's a countdown for midnight and a firework display will also take place. These events are free, so well worth joining and taking in the atmosphere and good vibes! These public events can be very well attended; Dalmatian newspaper Slobodna Dalmacija claims that 70,000 people welcomed in the New Year in Split on the Riva in December 2010!
As you're probably aware, Croatia doesn't (yet?) have a year-round tourism industry, although - little by little - the season is being extended and more and more hotels are staying open year-round. (Or some re-open for the Christmas and New Year period.) Many offer special deals for stays during this period - check on hotel websites to see prices for stays at this time and what festivities they have planned!