The "school" set I mentioned earlier was reproduced from English Folk Songs for Schools (Sabine Baring Gould and Cecil Sharp , 1905); the text may be collated.  The tune appears to be that noted by Sharp from Mrs. Lucy White of Hambridge, Somerset, in 1904, though with the rhythm made more regular.  Here is her version:

THREE JOLLY HUNTSMEN

(Noted by Cecil Sharp from Mrs. Lucy White of Hambridge, Somerset, in 1904.)

We hunted all the day, my boys,
But nothing could we find
But a hay-rick in the fields, my boys,
And that we left behind.
The Englishman said: Hayrick,
The Scotchman he said: Nay,
Poor Paddy said: It's the Catholic Church
With the steeple blown away.
And a-hunting we will go.

So we hunted all the day, my boys,
But nothing could we find
But a hedgehog in the fields, my boys,
And that we left behind.
The Englishman he said: Hedgehog.
The Scotchman he said: Nay.
Poor Paddy said 'twas a pincussion
Turned up the upside way.
And a-hunting we will go.

We hunted all the day, my boys,
But nothing could we find
But a black pig in the field, my boys,
And that we left behind.
The Englishman he said: Black pig.
The Scotchman he said: Nay.
Poor Paddy said it was Old Nick
And so let us run away.
And a-hunting we will go.

From The Crystal Spring: English Folk Songs Collected by Cecil Sharp, ed. Maud Karpeles, Oxford University Press 1975.  The Welshmen often become, in later versions, an Englishman, Irishman and Scotsman.  Peter Kennedy printed one such set from Hywel Wood of Bala, Merionethshire, 1954, Three Men Went a-Hunting, and wondered whether the change might be the revenge of the Welsh!

 A midi of the Mrs. White's tune will appear at  The Mudcat Midi Pages  in due course, but can meanwhile be heard via the  South Riding Folk Network  site:

Click to play Three Jolly Huntsmen.