Two terms need to be defined here. These from "Western Words, 1944, Ramon F. Adams, p. 79:
1. hooyey-ann- "A roping term. This throw can be made either from the ground or on horseback. The roper carries the loop in his hand, and when the chance presents itself, he swings one quick whirl around in front of hi, toward the right, up over his head, and releases the loop and rope in the direction of the target. Asd it comes over, it is turned in a way to cause it to flatten out before it reaches the head of the animal to be roped. It lands straight down, and so has a fair sized opening."
"It is a fast loop and is strictly a head catch, being especially used to catch horses in a corral."

2. hoolihaning- "The act of leaping forward and alighting on the horns of a steer in bulldogging in such a manner as to knock the steer down without having to resort to twisting him down with a wrestling hold. This practice is barred in practically all recognized rodeos.
Also to throw a big time in town- to paint the town red."

Donald Gilbert y Chavez, author of "Cowboys-Vaqueros, Origins of the first American Cowboys," has an extensive glossary of Vaquero/Cowboy Lingo, but does not include either term, so it is likely neither is of vaquero origin.
His booklet has been put on line by the University of New Mexico: Vaquero Lingo

Most of this is in another thread, but not certain which one.