Not strictly 'about' Yorkshire - but it gets a mention right up front . . . 'Female Drummer' . . .

'I was brought up in Yorkshire and when I was sixteen' etc

Steeleye's version (Please to see the King) - with surely the best folk-rock riff ever!!! - was the very first bit of 'folk' that grabbed my attention way back when I was in the sixth form.

Also, Mel, you didn't say if the songs had to be trad.
For example, there's the 'Yorkshire Couple' - a witty ditty that I've heard sung by Kate Rusby amongst others!
I forget who wrote the lyrics (Marsden?) - no doubt there's a more knowledgeable Catter that'll put that right here soon enough!.
That song (tying nicely in with my opening gambit) is sung , I believe, to the 'other' version of the tune of 'Female Drummer' I've heard - as sung by Harry Cox. (Help me out here someone?)