Do Mormons own the Cracker Barrel?

No. Cracker Barrel is a publically traded Stock Market company and is therefore owned by individual share holders. Some of the share holders might be Mormon, though.

Cracker Barrel was founded by Dan Evins in Tennesee. He is not a member of the Church of Jesus Christ of Latter-day Saints (the "Mormon" church) either.

The Church itself has never had any relationship with Cracker Barrel.