The genomic changes underlying both early and late stages of horse domestication remain largely unknown. We examined the genomes of 14 early domestic horses from the Bronze and Iron Ages, dating to between similar to 4.1 and 2.3 thousand years before present. We find early domestication selection patterns supporting the neural crest hypothesis, which provides a unified developmental origin for common domestic traits. Within the past 2.3 thousand years, horses lost genetic diversity and archaic DNA tracts introgressed from a now-extinct lineage. They accumulated deleterious mutations later than expected under the cost-of-domestication hypothesis, probably because of breeding from limited numbers of stallions. We also reveal that Iron Age Scythian steppe nomads implemented breeding strategies involving no detectable inbreeding and selection for coat-color variation and robust forelimbs.