This is a word that falls firmly into the category of invention for invention’s sake, since it refers to the craft of cutting white horses on hillsides. The count of carved figures of any kind is quite small, the number of horses even fewer, and their rate of creation is as near zero as makes no difference.
The oldest example of the genre in the UK is probably the white horse at Uffington in Berkshire, which has been dated, cautiously, to the late Bronze Age. Apart from one in Aberdeenshire and another in Yorkshire, most hillside horse carvings are on the chalk of southern England, with the biggest concentration on the Wiltshire downs. Leucipottomy has had an airing recently because the citizens of Devizes in that county decided that they wanted a white horse of their own as a millennium project, which — after 10 days of carving — they now have.
The word would seem to have been coined by Morris Marples in his book White Horses and other Hill Figures of 1949. As many subscribers have pointed out since this article first appeared, Morris Marples was no Greek scholar. It looks as though it is formed from the Greek roots leuci–, white, hippo, horse, and the suffix –tomy. Unfortunately this last doesn’t mean cutting or carving, but refers to cutting out or excising (as in many medical terms such as hysterectomy), so it actually means cutting off or excising white horses, which isn’t the same thing at all. (And in any case, it’s short one p and has one too many ts.)
A better invention would be leucohippoglyphy or leucippoglyphy, but I can’t find any evidence that either of these has ever been sighted. But if you have an urge to describe this little-known craft, at least now you will be able to avoid Mr Marples’ mistake.