I work part time at the National Aquarium in Baltimore. I work in our Living Seashore exhibit, which is a touch pool with multiple animals, including horseshoe crabs. Horseshoe crabs are relatively easy to keep alive. We feed ours raw shrimp and mackerel and almost nothing else. Life support consists of bioballs, a skimmer, a sand filter, and a UV sterilizer. So again, basic biological and mechanical filtration. We've got so good at keeping them that we've actually had a lot of success raising them in captivity. The adults are very large, probably a foot long not including the tail:
Having said all that, I would not attempt to put one in a reef tank.
First, while they can survive at a wide range of salinity and temperatures, we have the most success in Atlantic temperatures (between 60*F and 68*F) and salinity closer to 30ppt (1.023 SG). Most reef tanks are kept outside these parameters. Second, they tend to be very messy. They're not the most thorough eaters, so you'll need to be very diligent about cleaning up after them. Even so, expect the nutrient level to be relatively high in the system. You'll need a relatively high level of biological filtration, which means a lot of live rock. However, don't plan on keeping the rock in the tank. They'll easily topple any reasonable rock formation you could hope to build.
If you have a large tank to dedicate to just a horseshoe crab and nothing else, they're fairly easy to keep alive. Otherwise, I probably wouldn't attempt it. I definitely would not personally put one in a reef tank. Some have tried, and I wouldn't be surprised if some of those were successful. I wouldn't though. Just my $0.02.