saddle seat
noun
: a slightly concave chair seat (as of a Windsor chair) with sometimes a thickened ridge at the center front
Example Sentences
Recent Examples on the Web The mezcal and tequila bar, Bodega Mezcaleria, stocked with the country’s artisan labels, remains open for sipping from sustainable coconut cups while straddling a saddle seat, whether on a noon or midnight whim. 
Lauren Mowery, Forbes, 16 May 2022 The American Royal is a show that is deep in tradition for saddle seat riders dating to its inception in 1905. Chris Barlow, Milwaukee Journal Sentinel, 7 Feb. 2018
Lauren Mowery, Forbes, 16 May 2022 The American Royal is a show that is deep in tradition for saddle seat riders dating to its inception in 1905. Chris Barlow, Milwaukee Journal Sentinel, 7 Feb. 2018 Word History
First Known Use
1895, in the meaning defined above