Awd Dicky Thompson, he had a grey mare
And he took 'er away ti Sedgefield Fair
But he browt her back, whoa yes he did
Because he hadn't a farthin bid

awd = old; ti = to; browt = brought
Dicky Thompson seems to be Mrs. Willy from Westerdale's cousin; they share the same light touch with livestock.
The dialect is North and East Riding, mostly.

Chorus (after each verse):
(Singin) Titty fa lairy, fire up Mary
Up to the jigs o' Sedgefield Fair

As A.L. Lloyd notes, “fire up Mary” may refer to a threshing engine. (Though at times the Watersons seem to be singing “fire off Mary”--suggested by Dicky's awd gun?)
jigs = pranks

Now he turned her away into Wragby Wood
He thowt his awd mare might deea some good
But she ran her awd head right intiv a tree
Gor dang, says Dick, t'awd mare'll dee

thowt = thought; deea = do;
intiv = into;
t'awd = the old; dee = die

Now he browt her some hay, it were all in a scuttle
And her poor awd belly began for to ruttle
So he browt her some corn, it were all in a sieve
Gor dang, says Dick, t'awd mare'll live

ruttle = rattle (a phlegmy cough is said to ruttle)

Now he took 'er away inti't field to ploo
To see what good 'is awd mare could do
But at every end, she give a great fart--
Gor dang, says Dick, we'll plough until dark

inti't = into the; ploo = plough

Now all of his sheep got intiv his fog
And he sent away home for t' black and white dog
And every end he give a great shout
It were, Get away by 'em and fetch 'em out!

fog = new grass which springs up after mowing
(There goes his second crop of hay.)

Then all of his hens got intiv his corn
And he swore he would shoot 'em, as sure he's born
So he got his awd gun and he squinted and squared
And he missed t'awd hens and he shot his grey mare