Anette: Nancy's comment hit the nail on the head, it's all about process or continuous action, versus a moment in time.
I can't speak for Irish English, but in standard English the line
"As I went home on a Monday night / as drunk as drunk could be / I saw a horse outside the door..."
would be incorrect. So in the song, yes they are using artistic license, since 'went' indicates a moment in the past, and 'as' requires continous action. In standard English, this would be:
"As I was going home on a Monday night... I saw a horse outside the door".
Compare "As I was going to St. Ives, I met a man with seven wives..." (http://ingeb.org/songs/asiwasgs.html
However, note that since the rest of the song makes it clear that he's talking about the door of his own house, although the reformulated version of the sentence with 'was going' would be grammatically correct, the verb choice is wrong; you would have to say "When I got home... I saw a horse" to correspond correctly to the meaning.