Numerous authors have claimed that willow was used by the ancients as a painkiller, but there is no evidence that this is true. All such accounts date from after the discovery of aspirin, and are possibly based on a misunderstanding of the chemistry. Bartrams 1998 Encyclopedia of Herbal Medicine is perhaps typical when it states, in 1838 chemists identified salicylic acid in the bark of White Willow. After many years, it was synthesised as acetylsalicylic acid, now known as aspirin.' It goes on to claim that willow extract has the same medical properties as aspirin, which is incorrect.
Ancient medical uses for willow were more varied. The Roman author Aulus Cornelius Celsus recommended using the leaves, pounded and boiled in vinegar, as treatment for uterine prolapse, but it is unclear what he considered the therapeutic action to be; it is unlikely to have been pain relief, as he recommended cauterization in the following paragraph (De Medicina, book VI, p. 287, chapter 18, section 10). Gerard quotes Dioscorides, that [the bark] being burnt to ashes, and steeped in vinegar, takes away corns and other like risings in the feet and toes, which is similar to modern uses of salicylic acid.  Translations of Hippocrates make no mention of willow at all.
Nicholas Culpeper, in The Complete Herbal, gave many uses for willow, including to staunch wounds, to stay the heat of lust in man or woman, and to provoke urine (if stopped) but, like Celsus, made no mention of any analgesic properties. He also used the burnt ashes of willow bark, mixed with vinegar, to take away warts, corns, and superfluous flesh.
Although Turner (1551) thought that fevers could be cured by cooling the air with boughs and leaves of willow, the earliest known mention of willow bark extract for treating fever came in 1763, when a letter from English chaplain Edward Stone to the Royal Society described the dramatic power of powdered white willow bark to cure intermittent fevers, or ague. Stone had accidentally tasted the bark of a willow tree in 1758 and noticed an astringency reminiscent of Peruvian bark, which he knew was used to treat malaria. Over the next five years he treated some 50 ague sufferers, with universal success, except in a few severe cases, where it merely reduced their symptoms. Stone's remedy was trialled by a few pharmacists, but was never widely adopted. During the American Civil War, Confederate forces experimented with willow as a cure for malaria, without success.