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If you have a TX CHL, no problem with your sidearm. OK & many other States
honor Tx CHLs.
Long guns should be no problem. No doubt, hundreds of rifles & shotguns cross the OK/TX border every day without interest by either State.
I expect you'd be wise to have a Hunting License for both States, though, if you're going hunting and expect to transport game back home...
Minnesota no longer honors TX CHL’s.