"tree planted or valued for its shade," rather than for fruit, beauty, etc., 1806, American English, from shade (n.) + tree (n.).
Entries linking to shade-tree
shade n.
Middle English shade, schade, Kentish ssed, "dark image cast by someone or something; comparative obscurity or gloom caused by the blockage of light," from late Old English scead "partial darkness; shelter, protection," also partly from sceadu "shade, shadow, darkness; shady place, arbor, protection from glare or heat." Both are from Proto-Germanic *skadwaz (source also of Old Saxon skado, Middle Dutch scade, Dutch schaduw, Old High German scato, German Schatten, Gothic skadus), from PIE *skot-wo-, from root *skoto- "dark, shade."
shade, shadow, nn. It seems that the difference in form is fairly to be called an accidental one, the first representing the nominative & the second the oblique cases of the same word. The meanings are as closely parallel or intertwined as might be expected from this original identity, the wonder being that, with a differentiation so vague, each form should have maintained its existence by the side of the other. [Fowler]
Figurative use in reference to comparative obscurity is from 1640s. Hence throw into the shade, etc., "obscure by contrast or superior brilliancy." The meaning "a ghost" is from 1610s; dramatic (or mock-dramatic) expression shades of _____ to invoke or acknowledge a memory is from 1818, from the "ghost" sense. Meaning "lamp cover" is from 1780. Sense of "window blind" is recorded by 1845. The meaning "cover to protect the eyes" is from 1801. Meaning "grade of color" is recorded from 1680s; that of "degree or gradation of darkness in a color" is from 1680s (compare nuance, from French nue "cloud"). Meaning "small amount or degree" is from 1749.
tree n.
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.