The phrase a horse that was foaled of an acorn denoted the gibbet, sometimes also called triple tree. In A Collection of English Proverbs (1678), the English naturalist and theologian John Ray (1627-1705) wrote:

You’ll ride on a horse that was foal’d of an acorn. That is the gallows.

Pelham; or, The Adventures of a Gentleman (1828), by the English author and politician Edward George Earle Lytton Bulwer-Lytton (1803-73), contains the following (Tyburn was the place of public execution for Middlesex until 1783, hence the allusive use of the name):

The cove is a bob cull [= nice fellow], and a pal of my own; and moreover, is as pretty a Tyburn blossom as ever was brought up to ride a horse foaled by an acorn.

In the chapter titled The Life of Haman of The Holy State and the Profane State (1642), the English historian and Church of England clergyman Thomas Fuller (1608-61), paraphrasing the Book of Esther, from the Old Testament, used wooden horse in the sense of gibbet. Haman, a vizier in the Persian Empire under King Ahasuerus, has by anticipation erected a gallows for Mordecai the Jew. But the king learns in the meantime that Mordecai has foiled a plot to murder him. He therefore raises Mordecai to a high rank and has Haman executed on the gallows erected for Mordecai. Thomas Fuller wrote:

Haman provides a gallows of fifty cubits high to hang Mordecai on. […] Mordecai’s good service was related; and Ahasuerus asketh Haman, newly come into the presence, “What shall be done to the man whom the king will honour?”
[…] By the king’s command he [= Haman] becomes Mordecai’s herald and page, lackeying by him, riding on the king’s steed (who he hoped by this time should have mounted the wooden horse). […]
Haman inherits the gibbet of Mordecai, and Mordecai the house and greatness of Haman.

In the chapter titled The Traitor, Thomas Fuller also used wooden horse to denote the rack, that is, an instrument of torture:

The rack, though fame-like it be
“Tam ficti pravique tenax quam nuncia veri*”,
is often used; and the wooden horse hath told strange secrets.

* “As greedy a messenger of falsehood and depravity as of the truth” – from the Aeneid, by the Roman poet Virgil (Publius Vergilius Maro – 70-19 BC)

Similarly, a wooden horse was a wooden frame on which soldiers were made to ride as a punishment. The English antiquary and lexicographer Francis Grose (1731-91) described this form of punishment in Military Antiquities respecting a History of the English Army: from the Conquest to the Present Time (1788):

Riding the wooden horse was a punishment formerly much in use, in different services. The wooden horse was formed of planks nailed together, so as to form a sharp ridge or angle about eight or nine feet long, this ridge represented the back of the horse, it was supported by four posts or legs, about six or seven feet long, placed on a stand made moveable by trucks; to complete the resemblance, a head and tail were added. The annexed plate will give a much better idea of it, than can be conveyed by words.

When a soldier or soldiers were sentenced by a court-martial, or ordered by the commanding officer of the corps, to ride this horse, for both were practised, they were placed on the back with their hands tied behind them, and frequently, to increase the punishment, had muskets tied to their legs, to prevent, as it was jocularly said, their horse from kicking them off; this punishment being chiefly inflicted on the infantry, who were supposed unused to ride. At length riding the wooden horse having been found to injure the men materially, and sometimes to rupture them, it was left off. The remains of a wooden horse was standing on the parade at Portsmouth, about the year 1760.

The term timber mare was used in the same sense, for example by the Scottish lawyer and historian John Spalding (1609-70) in Memorialls of the Trubles in Scotland and in England, 1624-1645 (circa 1650):

ane tymber meir, quhairvpone runnaget knaves and runaway soldiouris sould ryde.
translation:
a timber mare, upon which renegade knaves and runaway soldiers should ride.