saddletree (n.)

Middle English sadel, from Old English sadol "contrivance secured to the back of a horse, etc., as a seat for a rider," from Proto-Germanic *sathulaz (source also of Old Norse söðull, Old Frisian sadel, Dutch zadel, zaal, German Sattel "saddle"), from PIE root *sed- (1) "to sit" + Germanic suffix *-þra, used to form neutral names of tools.

Extended to various things resembling or functioning as a saddle. Figurative phrase in the saddle "in an active position of management" is attested from 1650s. Saddle-horse "horse for riding" is from 1660s. Saddle-stitch (n.) is from bookbinding (1887).

Old English treo, treow "tree" (also "timber, wood, beam, log, stake"), from Proto-Germanic *trewam (source also of Old Frisian tre, Old Saxon trio, Old Norse tre, Gothic triu "tree"), from PIE *drew-o-, suffixed variant form of root *deru- "be firm, solid, steadfast," with specialized senses "wood, tree" and derivatives referring to objects made of wood.

The line which divides trees from shrubs is largely arbitrary, and dependent upon habit rather than size, the tree having a single trunk usually unbranched for some distance above the ground, while a shrub has usually several stems from the same root and each without a proper trunk. [Century Dictionary]

In Old English and Middle English also "thing made of wood," especially the cross of the Crucifixion and a gallows (such as Tyburn tree, famous gallows outside London). Middle English also had plural treen, adjective treen (Old English treowen "of a tree, wooden"). For Dutch boom, German Baum, the usual words for "tree," see beam (n.).

Meaning "framework of a saddle" is from 1530s. Meaning "representation of familial relationships in the form of a tree" is from c. 1300. Tree-hugger, contemptuous for "environmentalist" is attested by 1989.

Minc'd Pyes do not grow upon every tree,

But search the Ovens for them, and there they be.

["Poor Robin," Almanack, 1669]