Fair Park is owned by the City of Dallas, they cannot restrict carry per Texas Law. It is a pain to carry during the Fair becuase they take down you license information and make you wait for a supervisor, however it is definately possible as my wife and I have done it multiple times.
Glock 22,26,33,34 Beretta 92FS, Taurus.357
Bersa Thunder .380, Keltec P3AT/P32
Beretta AL391 Trap, Ruger Mark III
Tokarev TT33, AK-47, Rock River AR15
Sin Moo Hapkido, Arnis De Leon