Here is some info from some various web sources (so who knows exactly how accurate):
Italy, too, a very Christian country, has many foods and rituals surrounding Christmas, such as the ritualization of lasagne for Christmas. Many ritual foods have a long history, such a mortadella for Christmas, as we know because mortadelle is mentioned in the statutes of the Cathedral of Nice from 1233 as being made for holidays such as Easter, pentecost, or Christmas along with meat and beans. A famous preparation for Christmas Eve on the island of Burano in the Venetian lagoon is a risi e fasjoi col brodo de gò, rice and beans with a broth made of goby.
http://www.cliffordawright.com/history/christmas.html
The Christmas season in Italy, which lasts for three weeks, begins with the Novena. The Novena is the period of eight days prior to Christmas Day and is an exciting build-up to that special day. It is filled with music and laughter. It is traditional during this period for groups of young musicians to go around the neighborhood playing their musical instruments and singing Christmas Carols and reciting Christmas poems. Sometimes the musicians dress up as Shepherds, sometimes the performers are real Shepherds, dressed up in the rustic style of olden days. They perform at every house along their route and after each performance the house owner usually offers each of the performer a monetary gift in exchange and this money is later on used to buy gifts.
All the necessary preparations for Christmas are also made during the Novena. In Italy, Nativity Scenes are very popular and can be seen displayed in almost every Christian household. In fact the tradition of having Nativity Scenes began in Italy first and traces its origins back to St. Francis of Assisi and Giovanni Vellita, a work-man from the village of Greccio. Apparently St. Francis came up with the idea of performing mass before a recreated version of the Nativity Scene and asked the above mentioned Giovanni Vellita to construct a scaled down model for him.
http://www.buzzle.com/editorials/12-23-2004-63380.asp
Bagpipes are the most common Italian Christmas sound. The zampognari, the shepherds who play the bagpipes, come down from their mountain homes at Christmas time and perform in the market squares. The playing of bagpipes is popular in the regions of Calabria and Abruzzo, and in the piazzas of Rome. The melodies played are adapted from old hill tunes. Modern zampognari wear the traditional outfits of sheepskin vests, leather breeches, and a woolen cloak. The tradition of bagpipes goes back to ancient Roman times. Legend says that the shepherds entertained the Virgin Mary in Bethlehem. During the holiday season. Today, the zampognari stop before every shrine to the Madonna and every Nativity scene.
Children in Italy believe in a female version of Santa Claus called La Befana, an old woman who flies on a broom and brings presents. According to Italian legend, Three Wise Men asked La Befana for directions to Bethlehem. La Befana was asked to join them but declined three times. It took an unusually bright light and a band of angels to convince La Befana that she must join the Wise Men, but she was too late. She never found the Christ child and has been searching ever since. On January 6, the Feast of Epiphany, La Befana goes out on her broom to drop off stockings filled with treats to all the sleeping children of Italy. Just as children in America leave milk and cookies for jolly Santa Claus, La Befana collects messages and refreshments throughout the night.
http://www.initaly.com/regions/xmas/xmas.htm
Well, I couldn't find much related strictly to Venice, but Italy is close enough, no? In any case, Buon Natale!