Once again, the net doesn't lie...

Most gold medals (horse)

Rembrandt was ridden by Nicole Uphoff in all four of her medal winning rounds-- two individual titles and two team titles, both in 1988 and 1992.
(link above)

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Most gold medals (horse)
The most successful horse is Halla, ridden by Hans-Gunther Winkler during his individual and team wins in 1956, and during the team win in 1960.

Guinness Book of World Records

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I'm learning a bit about dressage and show jumping...