I’ve never heard of an antlion before, so I looked it up and yikes! I can see why you wouldn’t want them around, especially if your horse is allergic. Unfortunately, because they aren’t harmful to plants or people, I couldn’t seem to find any information on getting rid of them (most gardeners consider them to be beneficial!). If I were you, I’d reach out to your local Cooperative Extension Center (http://www.csrees.usda.gov/Extension/). They know your area best, and may have some helpful advice.
Rider, Runner, Stuff-Riders-Say-er, SmartPaker