Actually no. 'drawing and quartering' or 'drawn and quartered' is an American English idiom meaning to be 'severly punished'. The expression alludes to, and is derived from the old English punishment for treason, but is not actually the punishment itself. The correct term for which is hanged, drawn and quartered.
And please note that this does not involve the use of trees. This is England we are talking about, not the Wild West. Judicial hangings (whether accompanied by drawing and quartering or not) were carried out on a properly erected scaffold. And no horses; quartering by horses in this manner was never carried out in England. It was the French that used to perform executions in this manner.
Michel Foucault provides a description of one such quartering in his Discipline And Punish 1. From this and other accounts of similar executions it appears that the French practice of quartering by horses was never very successful.
And the idea that the quartering was done so that the body could be buried in the four corners of the realm sounds like and old wives tale to me.
For one thing there were five body parts to deal with not four (don't forget the head). Secondly they were never buried, they were placed on public display and allowed to rot away. Which was the point of the exercise, getting an assortment of body parts to put on public display so that everybody got the message. (I've no idea what happened to the remaining bones, probably boiled down for glue I should imagine.)
For example that arch-criminal William Wallace who was hanged, drawn and quartered in 1305 had his head was displayed in London. His body parts however were sent to Newcastle (right arm), Stirling (left arm), Berwick(right leg) and Perth (left leg), which are all of course in one corner of the realm.
Of course in Wallace's case one of his arms is supposed to have been 'liberated' by the monks from Cambuskenneth Abbey and buried in the Abbey grounds pointing in the direction of the site of his great victory at Abbey Craig. But that's only tradition and no one actually knows what happened to his body. Which is the case with the most people who were hanged, drawn and quartered. They were either rebellious Scots or Welsh or religous dissidents, the authorities wanted to eliminate all trace of them. The last thing they would have wanted was four little shrines dotted about the country.
1 See http://web.ics.purdue.edu/~felluga/punish.html for example.
2See the The American Heritage Dictionary of Idioms by Christine Ammer at http://www.xrefer.com/entry.jsp?xrefid=631071