You can cook meat. It's not very intuitive unless you are familiar with The Long Dark. I've been meaning to add some text or a tutorial objective to help explain it and possibly a way to add meat to the fire with buttons in the fire menu.
To cook meat, you must first drop it from your inventory, then pick it up with the right mouse button. When you do so, two circles will highlight near the front of the fire. While holding the meat, move it to one of the highlighted circles. The meat will snap into place and begin to cook. You will not be able to pick it up again until it either cooks fully or the fire goes out before it is done.