The traditional, and cheaper way, to filter wine is with the following animal driven Ingredients:
therefore if used, it is not vegan. Sometime it changes from year to year, which can be difficult to follow.
An example of a company that keeps their info up to date is "Sutter Home". They are inexpensive and widely available in the U.S.
Today a lot of vineyards use an electric filtration systems.
A good resource to check changes is Barnivore at barnivore.com