Dry lots---no grass---and feeding up off the ground does minimize parasite reinfection rates. This is because your horse is not eating from the area where parasite larva are.
Grazing---eating grass that is growing in the ground--is the biggest risk factor for parasite infection. Horses are such parasite magnets because they spend so many hours eating grass each day if they are pastured animals. If they aren't eating contaminated grass, then they pick up much fewer parasites. By dry-lotting and feeding everything up off the ground you take out the biggest factor in parasite infections.
Without grass, the risk of tapeworms drops to pretty much nil (there might be some contamination in hay so there is still a possibility) because you have to have grass mites to have tapeworms. No grass=no grass mites.
Strongyles also are transmitted more readily when there is grass in a pasture because somee larva actually migrate up the blades in order that they may be more readily ingested and it's the grazing and picking up feed off the ground that allows for parasite larva to be ingested.
Horses do not genrally eat manure even in a dry lot. The problem with manure arrises when it's in a grazed area because the larva migrate out a short way from the manure and can get washed out or spread out by breaking down of the manure and thus get into the grass so that they can be eaten. In a dry lot, even when manure is left you have minimal "picking up" of forage off the ground so minimum risk of reinfection. https://www.thehorse.com/ViewArticle.aspx?ID=359
"Infection from stalls or dry-lot paddocks is negligible--clean horse stalls are simply too dry to allow strongyle larvae to develop or persist, and even in a filthy, damp stall, strongyles are unlikely to develop because the ammonia that comes with urine accumulation is extremely toxic to strongyle larvae. Clean and dry or wet and stinky, horses rarely acquire new strongyle infections in confined conditions. " http://www.thehorse.com/ViewArticle.aspx?ID=1523