saddle-tree

/S AE1 D AH0 L T R IY0/
noun
  1. 1

    The base on which the rest of the saddle is built. Usually based on wood or a similar synthetic material, it is eventually covered in leather or a leatherlike synthetic. The tree size determines its fit on the horse's back as well as the size of the seat for the rider.

  2. 2

    The tulip tree.

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Source: https://en.wiktionary.org/wiki/saddle%20tree, https://en.wiktionary.org/wiki/saddle-tree