Okay, let's clear this up once and for all:

Oh, they say 1) she died one winter
When there came a killing frost
And 2)the pony she named Wildfire
Busted down its stall
3) In a blizzard he was lost

4) She ran calling Wildfire x 3
By the dark of the moon I planted
But there came an early snow
There's been a hoot-owl howling by my window now
For six nights in a row
She's coming for me, I know
And on Wildfire we're both gonna go
---------
Right. In chronological order we have 1) she died of a killing frost, just like a tomato plant.

2) Her horse seemed to sense the tragedy and broke down its stall door

3) A blizzard came, and the horse got lost. The frost must have been the first sign of the blizzard to come. That's pretty fast action, even for Nebraska, when a killing frost is expected in September and blizzards in January or February.

4) She ran calling "Wildfire," but she's already dead. See #1. So it's her ghost that's calling. The singer predicts that she will snatch him away and they both will become ghosts, riding on Wildfire's ghost.

Ornithological note: the hoot-owl, another species not in the bird books, can join the chicken hawk and the mudcat. See the thread about eating a mudcat.