Among the family of velvet ants is a wasp called the “cow killer", which has conspicuous red coloration that presumably wards off potential enemies. Given that the venom of Dasymutilla occidentalis is measurably less toxic than that of honeybees and harvester ants, it is absurd to think that the sting of these noncolonial hymenopterans is lethal to vertebrates. Furthermore, females are nonaggressive and male velvet ants lack a functional stinger all together.
Still, if handled or stepped upon, a female velvet ant will sting in self-defense. So perhaps the species' bright coloration does serve as a warning, enough to minimize the chance of being crushed from above. Unlike most wasps, female velvet ants cannot fly and spend most of their time searching the ground for nursery burrows of insects, such as digger wasps and bumble bees. When a burrow is located, a female will dig down to the host's pupa and lay an egg.* Given that suitable burrows in which to lay her eggs are either well hidden and/or widely distributed may explain why a female is so active in her search.
In Florida, I have encountered females of several species of velvet ants and all lacked wings. Males, on the other hand, can fly, which is an ability that presumably helps them locate females. In their nuptial search they fly back and forth over promising terrain while frequently landing to sample the air for pheromones released by receptive females.