Round sand particles interact like a zillion tiny balls so do not provide the stability required for a horse's landing, loading, and push-off. Beach and riverbed sand is often too spherical for arenas. Glacial sand, with its irregular angular surfaces, results in a more interlocking particle interaction and therefore better stability and traction. Sand also varies in mineral content. Sand containing quartz resists breakdown so is long lasting.
Sand containing feldspar and mica breaks down relatively quickly.
Cheap sand has a high silt and clay content which is referred to as fines. Fines are just that, fine particles or dust just waiting for a place to cause a problem. Fines create dust and tend to pack which inhibits drainage. Sand can also contain small gravel or stones. Unlike clay, sand has more strength when it is wet, in fact, it often becomes too hard.