Skite may mean getting drunk (esp in NZ) but it also means to throw or squirt liquid:
Skyde, skyte, skite (v) = to splash or squirt liquid, to slip (as on ice).
Skide (v) = to slide
Shite (n) = Shit
See the online Scots Dictionary for any of these (or other) words:
The root of the word is northern European: O.N. skyt-, the stem of skjóta, to shoot, propel, dart, Norw. skyte , Dan. skyde, to shoot.
An event referred to as a "Skite Night" took place once a year among St Andrews University students in 1961. Informally organised - not an official student event. It was banned around 1961 or 1962 after the disorderly events caused local upset.
During a skite night the main activity was running around wildly throwing flour and water at each other. Naturally the streets became messed up. However, "Skite Night" must have been revived and still goes in St A see the third link above.