Real Dictionary

horse chestnut
countable noun: Horse chestnuts are the nuts of a horse chestnut tree. They are more commonly called conkers.
variable noun: A horse chestnut is a large tree which has leaves with several pointed parts and shiny reddish-brown nuts called conkers that grow in cases with points on them.

horse chestnut in American English
any of a genus (Aesculus) of shrubs and trees of the horse-chestnut family, including buckeyes; esp., a tree (A. hippocastanum) with large, palmately compound leaves, clusters of white flowers, and glossy, brown seeds
noun: a tree, Aesculus hippocastanum, native to the Old World, having digitate leaves and upright clusters of white flowers

horse chestnut in British English
noun: any of several trees of the genus Aesculus, esp the Eurasian A. hippocastanum, having palmate leaves, erect clusters of white, pink, or red flowers, and brown shiny inedible nuts enclosed in a spiky bur: family Hippocastanaceae

horse-chestnut in American English
designating a family (Hippocastanaceae, order Sapindales) of dicotyledonous trees, including the horse chestnuts