WordNet records no synonym and no antonym for sidesaddle. It is the only member of each of its synsets, which is common for technical, taxonomic and single-sense vocabulary — there is no other English word that means the same thing. The broader and narrower terms below are the useful relations in that case.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
a saddle for a woman; rider sits with both feet on the same side of the horse
1 of the 2 recorded senses carries no synonym, antonym or related term, so it is not shown above. Every sense, with its definition and examples, is on the full entry for sidesaddle.
Synonyms, antonyms and the broader and narrower relations for sidesaddle come from Princeton University’s WordNet. Full sources and licences.