The tomb of St. Nicholas of Myra had long been a popular pilgrimage destination, but when sailors from Bari, Italy stole his relics from the Turkish-occupied town, devotion to St. Nicholas took off in the west. Given the stories of his generosity and his love for children, it was natural that St. Nicholas should surround himself with the aura and the legends of Father Christmas, a lingering memory of Norse legend. Within a couple of hundred years, the Feast of St. Nicholas was a landmark in the Advent season, hailing the election of the Boy Bishop (more on this character later) and the exchange of Christmas gifts.
Since my childhood was not spent in the Church, the first time I encountered any celebration of St. Nicholas’ Day was when I visited my soon-to-be wife’s family. Later, when we lived in Gaming, Austria, we experienced the intensity of medieval devotion to St. Nicholas. A friend who was a boy in Gaming around that time has posted his vivid memory of Nicholas and the Krampus here–you can see what I mean by “intense”! Our first daughter was a baby at the time, and we realized that we just had to stay inside. Krampus was too much.
Once back in the states, we brought new fervor to our celebration of St. Nicholas’ Day, although we haven’t opted to have a demon chase our children with whips. Instead, we bought a giant cookie mold of the bishop Nicholas from houseonthehill.net; since the cookies need time to age, we make them a couple of weeks ahead of time. The night of December 5, the kids make gingerbread cookies for their stockings.
In the morning, the stockings are hung by the fire place–the 
beautiful, hand-crafted stockings my mother has lovingly made for each child–and in the stockings are cookies, some chocolate coins to remember the story of St. Nicholas’ gifts, and a small gift. Typically, the stockings buy time for my wife and me to get up slowly and make breakfast at a more leisurely pace.
In the afternoon, we’ll make hot cocoa and eat the giant Nicholas cookies. I like to give at least one giant cookie away, if I can. Because I’m into medieval customs these days, our background music will be an album of medieval folks songs for the feast of St. Nicholas.
After reading your friends post about Krampus I think Krampus would be WAY to intense for me… let alone my girls! My 7-year-old would have nightmares for weeks! We do not do the cookies but we do everything else you mentioned in your post. We also do “Santa Claus” on Christmas (which is the exact same tradition for us as St. Nicholas) and the girls know that Santa and St. Nicholas are the same person. The reason I like the Christmas morning tradition is it buys me time to cook a leisurely breakfast.