Since the new queens-to-be have wings, it means that ants either evolved from insects that can fly, or insects that can fly evolved from ants, or that we have a case of parallel evolution (which is unlikely).
Now, what evolutionary benefit is there to not have wings?
Certainly ants evolved from insects that could fly. All the earliest wasps (ants are specialized wasps) could fly.
Building and maintaining wings is expensive in terms of energy. That's an obvious evolutionary advantage to not having wings. So if there's insufficient benefit from having wings then there's selective pressure against having wings.
Building on Noah Snyder's answer…
Having wings could also be expensive in other ways. For example, energy aside, maybe the growth of wings relies on some special nutrients, which were scarce in the environment of the first ancestors of modern ants. So the ant colonies that grew smaller wings (or no wing at all) thrived.
Having wings could also cost them their lives. Maybe the workers in ancestor colonies used to be small and had a tendency to get stuck in spider webs (not having enough in-flight momentum or brute strength to break off the web), and somehow the queens and drones are less affected (because they don't tend to go to the same places as the workers to begin with, maybe; but that's unlikely: I see plenty of queens stuck in spider webs in Hong Kong in the mating season).
In fact, I believe the nutrient-driven path is quite likely. When you think about it, there is a huge behavioural component to this trait. If I remember correctly, all female ants are equal at birth. Whether a certain female becomes a worker, a soldier, or a queen depends on what it is fed as it develops. So the scenario could be that some ancestor colonies arrived in a place that didn't have an abundance in nutrients for wings. Some of those colonies tended to reserve the said nutrients to the reproductive casts (queens and drones), and this strategy proved successful, so the trait got amplified over time. So it becomes a matter of less wings, not smaller wings.
When you need to move a great distance in as short a time as possible with minimal risk.
Clearly wings would have enormous benefit at a time when you need to get far away from the nest really quickly, perhaps at a time when you believe the weather would be particularly favourable. This benefit increases exponentially when procreation is involved.
Almost any other time.
Rain and wings just do not go well together. If you get hit by a raindrop while wearing wings you are basically stuck where the drop lands until it evaporates completely.
I rest my case.
Agility, while wearing wings, just cannot be considered one of your evolutionary advantages.
Surely an ant trying to carry a piece of a leaf, however small, would consider wings a severe burden.
The protein investment in wings would surely be better spent on survival when food is scarce.
Wings make you incredibly easy to grab hold of in mid-air, unless of course you can shed your wings when stressed, and many ants can (while obviously butterflies and moths cannot).
Surely my arguments suggest that having no wings would be a serious advantage in almost any situation except on the rare occasion when you need to move a long way really fast. Clearly the ant has an amazing skill to only have wings when they are needed and not at any other time.
Added after a number of comments
You have to remember that much of an ant's work is maintaining the colony as a collective. Preserving its cohesion, feeding the young, caring for eggs. The whole point of having a colony is to have far fewer individuals spread out, in danger, gathering food. This is to reduce the risk of complete colony death, which is essentially the death of the queen and therefore the gene pool of the colony.
You have to look at each ant colony as a single individual when you look at them on an evolutionary scale. In this way the life or death of one, or even 1,000 ants is not important, it is the survival of the colony. From this perspective, wings are dangerous for all my reasons above. The only time they are of value is during diaspora and that is the only time ants have them, which I think is incredibly clever.
Evolving a detachable appendage to an ant is like humans evolving detachable breasts at menopause. An astonishing achievement even humans have failed to achieve.
