I found something close, The beauties of melody, by W.H. Plumstead, 1827, pp. 293-297 (similar verse bolded)

The Woodman
A favorite song, composed by Mr. Lindley

Stay, traveler, tarry here tonight;
The rain yet beats, the wind is loud,
The moon has too withdrawn her light
And has gone to sleep behind a cloud.

'Tis seven long miles across the moor
And should you chance to go astray,
You'll meet, I fear, no friendly door,
Nor soul to tell the ready way.

Come, dearest Kate, our meal prepare
This stranger shall partake our best,
A cake and rasher be his fare
With ale that makes the weary blest.

Approach the hearth there take a place,
And till the hour of rest draws nigh,
Of Robin Hood and Chevy Chase, *
We'll sing, then, to our pallets hie.

(Vivace)
Had I the means I'd use you well,
'Tis little I have got to boast;
Yet should you of you this cottage tell,
Say Hal the woodman, was your host
Say Hal the woodman, was your host


* The Chevy Chase of agricultural Maryland (link) and not the actor