It is often easy to find winged queen and male ants leaving the nest for their mating flights.
It is a whole different experience to actually see the mating swarm. If you have never seen a Pogonomyrmex mating swarm, the Social Insect Research Group at Arizona State University has a very cool video of a Pogonomrmex barbatus mating swarm on their website. (Note: it does take a long time to load).
Let me know what you think.