No, Jon Snow does not die. I read all books until now (2013) and he's not dead.
Jon Hol died in 1941.
Jon Douglas died in 2010.
Jon Vislie died in 1945.
Jon Kuvlung died in 1188.
Jon Petrovich died in 2011.
Jon Latimer died in 2009.
Jon Fossum died in 2007.
Jon Bilbao died in 1994.
Jon Marks died in 2007.
Jon Eardley died in 1991.
Jon Whitcomb died in 1988.
Jon Gjerde died in 2008.