When we butcher as soon as we get done gutting and cleaning them. They go in a cooler full of ice and salt. These are usually a 10 to 12 week old broiler or cx's meat bird. I don't know if this is what you are calling "brine" but it is what we do.
After they soak a bit we piece them out or put them whole in freezer bags and they go in the freezer or we take them to get smoked. When we take them to get smoked we leave them in a cooler with bags of ice to keep them chilled.
We mix up our brine and then add ice-cubes to bring the temps down - put the birds in then put it in the refrigerator for 2-3 days. There's lots of salt, plus other yummy ingredients. But DH has more experience/knowledge about it ... I just do what he instructs me to do.