In addition to Father Ted and Dougal, with their "My Lovely Horse" (which I guess is the one posted by Suibne, tho' I can't see the clip), there several other Irish ones: I've heard one called "Horses and Plough", and another called "The Mowing Machine", which struck me as very pleasant and moving (I don't have the words), and then there's Percy French's "Sweet Marie", which begins:

I've a little racing mare called Sweet Marie,
And the temper of a bear has Sweet Marie;
But I've backed the mare to win,
And on her bet all my tin,
So we'll take a trial spin, Sweet Marie---

Hold yer hoult, Sweet Marie!
If ye boult, Sweet Marie,
Ye'll never win the Farmers' Cup for me;
And if ye don't pull it through,
Faith! I'm done -- and so are you,
For I'll sell ye off for glue, Sweet Marie.