Warbird ride programs have varying costs. For me, the cost is usually to the aircraft operators. Because I am the photographer, I usually get paid to do this. Not that it isn't fun, but it is work too. Now that I think about it, I have only had one warbird "ride" in the last 10 years without the camera.
Some organizations, like the CAF, will give rides to volunteers as a way of thanking someone for the hard work. But the people who give the most get priority, which makes sense.