The traditional Yule or Saturnalia was all about fertility, and traditional Yule foods reflect that. Yule festivities typically consist of a ton of food, a celebration of the harvest of the year, and a demonstration of abundance.
Yule Log
Although the Yule Log is traditionally an actual log that is actually burned in the fireplace, the term also came to denote log shaped chocolate cakes which were served at Yule. Also called Buche de Noel, this French dessert was traditionally made by baking a yellow sheet cake, rolling it up like a log, and frosting it. I found an excellent Betty Crocker Yule Log recipe here. (It calls for cake mix, but I'm sure you can follow the directions with a "from scratch" cake if you prefer.)
Wassail, Mulled Cider, and Mulled Wine
Wassail is an ancient drink, most similar to the modern hot spiced cider. The original wassail was commonly a mildly alcoholic drink, something halfway between ale and grog. Wassailers would add sugar, ginger, nutmeg, and cinnamon, then heat the concoction to lend it a heady warmth.
Modern mulled cider can be easily prepared on the stovetop, using apple cider and a number of handy ingredients. And as a bonus, it smells absolutely delicious!
And don't overlook mulled wine! Mulled wine is wine prepared the same way as wassail or mulled cider. Simply add a bit of sugar and spices to taste, and heat gently.
Roasted Chestnuts
Roasted chestnuts are a classic solstice treat, and have even been entrenched in Christmas carol. Just be sure that you use the right chestnuts - horse chestnuts (common here in the Pacific Northwest as a decorative tree) are actually deadly poison, and nearly killed Penny Arcade.
Roasted Meats
Are you sensing a trend? Food at the winter solstice should be warm, and roasted as long as possible - not only to release the flavors, but also to tenderize "difficult" meats. And as with the mulled beverages, a roasting cut of meat makes the house smell delicious!
This page on Yule recipes traditional to Iceland lists several roasted meat recipes.
Yule Bread
Yule bread began as an Irish tradition, and was spread to the Scandinavian countries, where it remains a tradition. Many Yule bread recipes are simply Irish soda bread in a slightly different form, often with some currants or bits of candied orange peel. For example, Grandma's Danish Yule Bread recipe includes raisins, dried cherries, dates, and citron.
Fruit Cake
Yule bread is NOT the same thing as fruit cake, although you might be forgiven for thinking so. In fact, fruit cake shares a common heritage with Yule bread, but it was more common to southern and central Europe. Fruit cake is Yule bread gone wild - more packed with fruity bits, and often soaked in rum or other liqueur.