Saw in once in 1983 or 4
to predict the actual day I was told it was the first Mon after the first Sunday after 4th Sept but not every year. Bit like Easter there are clauses that were not specified that might delay it by one week.

The Wiki article prats on about magic rituals, but if you were an illiterate serf with deer hunting rights how would you re-iterate those rights? Much like yearly "Beating the Bounds" (done in a lot of places eg like Lichfield ) defines where the town/city/village was and the privileges and tithes that accrued to residency. Confusing rites with rights IMNSHO.
And the official pamphlet on the subject reckoned the reindeer horns were carbon dated to 1065 +/- 50 years (extinct here by then). And it points to a record from Lichfield cathedral of "dancers going out" in the 1300's without specific reference to horns in Abbots Bromley MAP

As for re-creating it in the colonies (or ex colonies to be PC) may I quote Martin Carthy (touches forelock) and transpose his quote from Folk Song.
"You can do anything to a custom, anything, and it will survive. Except ignore it"