The definition I've always heard for "hoolihan" (regardless of the spelling) jibes with the ones early in the thread — that it's a style of roping.As for going to Montana to do it, was it a technique used regionally? I know cowboys from different areas used different techniques (note the argument-song Windy Bill, which is based on how the cowboy takes his dallies (i.e. loops of the rope around the saddle horn). In the Texas style the loops are tight and the horse stops very quickly, yanking the cow off her feet. The California style uses looser loops and slows the cow more slowly.
Ely, I don't think there is any question that the lines you're wondering about refer to the Old Paint he rides and the Old Dan he leads. There's narry a mention of cows in that verse.
cheers,
david