Tall boots with a 1/2 inch heel is the norm show jumping. There are different varieties but the 2 basics are the 'field boot' and 'dress boot'. Field boots have lacing at the instep for easier on and off. Field boots are perfectly fine for most showing. Dress boots are for bigger shows, hunter classes, dressage. They a like field boots but are smooth all the way up with no lacing on the instep.
Stride-Rite Corp. makes Grasshoppers footware
Wolverine World Wide makes Caterpillar footware
Stride-Rite Corp. makes Munchkin footware
Deckers Outdoor Corp. makes footware
Stride-Rite Corp. makes Street Hot footware
Stride-Rite Corp. makes Stride-Rite footware
Stride-Rite Corp. makes Sperry Top-Sider footware
dressage, show jumping, and cross country jumping
Wolverine World Wide makes Coleman footware
Yes there was! There was Eventing and Jumpers. There was also dressage but that isn't show jumping.
Yes many horses do enjoy jumping.
Show jumping is also known as jumpers, stadium jumping, or open jumping. It is a member of a family of English riding equestrian events. The Enclosure Acts of England invented show jumping in the 18th century.