Here are the lyrics from Cowpie:

I ride an old Paint, I lead an old Dan.
I'm off the Mantan' for to throw the hoolihan.
They feed in the coulees,they water in the draw;
Their tails are all matted, their backs are all raw.

Chorus:
Ride a- round, little dogies, ride a-round slow,
For the fiery and snuffy are a-rarin' to go.

Old bill Jones had two daughters and a song;
One went to Denver,& the other went wrong.
His wife, she died in a poolroom fight,
And he sings this song from morning till night.

Oh, when I die, take my saddle from the wall,
Put it on my pony and lead him from the stall.
Tie my bones to his back,turn our faces to the west,
And we'll ride the prairies we love the best.^^^
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"I'm off the Mantan'" sounds nonsensical, I would have to say that's a misheard "I'm off to Montan'/Montana".

In the DT version, it has "...they're fiery and snuffy..." as mentioned by McGrath. However, there's also a note at the bottom indicating that some versions have the line "...the fiery and snuffy...", as mentioned by Metchosin and found on Cowpie. In either case, whether those words are adjectives or nouns derived from adjectives, it would sure be nice to know what "snuffy" means.

In some previous threads it was mentioned that one meaning of "hoolihan" was a melee of sorts. That would make sense if the lyrics were "..join the hoolihan..." or some such. Another meaning was a method of wrestling an animal down. That would make sense if the song said "...do the hoolihan..." or something similar. But "...throw the hoolihan..." really only makes sense to me if the hoolihan in question is a rope technique, as explained by Vince and Sorcha.