On or mounted upon a horse; in the state of riding a horse.
From the prefix 'a-' (meaning 'on' or 'in') combined with 'horse.' This archaic formation follows the pattern of Middle English adjectival constructions like 'afire' or 'aground.'
Words like 'ahorse,' 'afoot,' and 'aground' show how English once used 'a-' as a prefix to describe what condition you were in—it's efficient but sounds like Shakespeare now, which is why we don't use it much anymore.
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