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.
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.