After a little bit of research I've not only found an author for this rare but delightful song, but also discovered a fascinating connection to Handel. In so doing I have to disallow A.L.Loyd's claim in his notes to The Watersons LP A Yorkshire Garland that this is a Yorkshire song; it is in fact from Cheshire, though it probably survives better among the songs of the hunters in Yorkshire and Cumbria than in its native county.

The Gentleman's Magazine, Volume 17 January 1747 contains a 'Hunting Song, set to music by a gentleman of Wigan' on page 39 where the words and musical notation of A Hunting Song, by C.L. Esq. are given:-

A Hunting Song. By C.L. Esq;

The morning is charming, all nature is gay,
Away, my brave Boys, to your horses away:
For the prime of our pleasure and questing the hare,
We have not so much as a moment to spare.

Chorus
Hark the lively tuned horn, how melodious it sounds, how melodious it sounds,
To the musical notes, to the musical notes of the merry mouth'd hounds.

In yon stubble fields we shall find her below:
Soho! cries the huntsman! Hark to him; soho!
See, see where she goes, and the hounds have a view
Such harmony Handel himself never knew.

Cho. Gates, hedges and ditches to us are no bounds,
But the world is our own while we follow the hounds.

Hold, hold 'tis a double; hark hey! bowler hye!
If a thousand gainsay it, a thousand shall lye.
His beauty surpassing, his truth has been try'd,
At the head of the pack an infallible guide.

Cho. At his cry the wide welking with thunder resounds,
The darling of hunters, the glory of hounds.

O'er highlands and lowlands and woodlands we fly,
Our horses full speed, and our hounds in full cry,
So matched in their mouths and so even they run,
Like the turn of ye spheres and the race of the sun.

Cho. Health, joy and felicity dance in the rounds
And bless the gay circle of hunters and hounds.

The old hounds push forward, a very sure sign,
That the hare, tho' a stout one, begins to decline,
A chace of two hours or more she has led,
She's down, look about ye, they have her ware dead.

Cho. How glorious a death to be honour'd by [?] sounds,
Of horns, and a shout to the chorus of hounds.

Here's a health to all hunters and long be their lives
May they never be crost by their sweethearts or wives,
May they rule their own passions, and ever at rest,
As the most happy men, be they also the best.

Cho. And free from the care w[hich?] the many surrounds
See heav'n at last - when they see no more hounds.

Notes
The author,C.L., is Charles Legh (1697-1781) of Adlington Hall, near Macclesfield, Cheshire, while the music is by Mr Ridley the organist at Prestbury. The reference to Handel in the second verse is probably a family in-joke as Charles' elder sister, Elizabeth, had been a pupil of Handel, and the composer was a close friend of the family and almost certainly visited Adlington Hall on his way to Dublin for the first performance of the Messiah. More to the point Handel wrote a new musical setting to the song in 1751 (HWV 226), and the manuscript in his own handwriting is still in the possession of the family at Adlington Hall today.(Information from Handel at Adlington Hall.)

The song proved popular, and was reprinted in song collections such as Amaryllis, 1760, 'A choice collection of Favourite Hunting Songs', 1770 and 'The Vocal Enchantress', 1783.

Frank Kidson collected a version in 1902 from Mr Cropper at the Westmorland Musical Festival, which Roy Palmer printed in English Country Songbook, 1979.

The Holme Valley Beagles have included the song in their books of Hunters' Songs in successive editions since 1887.

The song also appears in the Songs of the Fell Packs published by the Melbreak Hunt in 1971.