The rule of thumb on stitching is 5-6 hours as far as the window goes before the flesh starts to die off. Waiting until the morning is going to make the healing process become a more intensive care cycle for you.
If there is any "inside" damage to joints, muscles, tendons etc then you are going to allow too much time for infection. My suggestion is also to call the vet immediately. Worse case send them a picture of the injury so they can decide if they need to come out asap. I think in this case - I would air on the side of caution, especially since the mechanism of injury was barbed wire. Those cuts aren't clean, they are kind of a puncture and then a snag. You also have to consider the need for a tetanus shot.
Please keep us informed.
Also - if the tendon WAS involved you are looking at a very long healing time (maybe even 6 weeks stall rest) not to mention the potential for permanent injury.
"Be a best friend, tell the truth, and overuse I love you
Go to work, do your best, don't outsmart your common sense
Never let your prayin knees get lazy
And love like crazy"