Hi Karin G,
I was also very confused at first because the festivals seem to be given different names. I visited the Ice and Snow World (as named on the entrance ticket) but most displays were made of ice with few sculptures made of snow. The entrance fee for this is 300 yuan. This is what most people visit in Harbin.
There is also a Snow Festival which is located in Sun Island Park (or otherwise known as Taiyangdao Park). The entrance fee to this is either 120 or 150 yuan.
The good news is that both places are close to each other. However, you will need to cross the Songhua River to reach them.
I don't know anything about the Lantern Art Fair. Now, there is another small park very close to the city centre with either models of snow or ice but it is not as big (or famous) as the two above.
I hope this helps, please let me know if you have any more questions.
Edited: 7:50 am, January 27, 2012