If you have a large open gash and basically no medical supplies, what do you do about that?

First stop the bleeding by applying pressure and then gently disinfect it (soap and water will work if you have nothing else).
Other than that, you can leave it open to the air as long as you wash it a few times a day. That is much better than wrapping it in something dirty (no medical supplies).
You'd be amazed at what a human body can cope with.