Harriet's Little Welsh Cow

"... she had spent two very happy months with them, and now loved to
talk of the pleasures of her visit, and describe the many comforts and wonders
of the place. Emma encouraged her talkativeness -- amused by such a picture of
another set of beings, and enjoying the youthful simplicity which could speak
with so much exultation of Mrs. Martin's having "two parlours, two very good
parlours indeed; one of them quite as large as Mrs. Goddard's drawing-room; and
of her having an upper maid who had lived five-and-twenty years with her; and of their having eight cows, two of them Alderneys, and one a little Welch cow, a
very pretty little Welch cow, indeed; and of Mrs. Martin's saying, as she was so
fond of it, it should be called her cow; "

Cattle born in the Welsh mountains were the stock of the droving trade, being herded down to eh midland pasturelands, fattened for several years, and then sent on to the London market. The Welsh Black wasn't really a developed breed in Jane Austen's time, although the commonest colouring was as in the picture above. These two cows, painted by Daniel Clowes in 1825, were named Bethal and Bran. They were owned by Sir Robert Vaughn , who was interested in developing the milking qualities of this breed. It may not be obvious in the scan, but Bethel and Bran have brass horn finials, presumably to make them a little less dangerous to their milkman!

Since Harriet is so emphatic about her 'little' cow, it just might be that it was of the kind known as an 'Anglesey Runt'. From:, A Topographical Dictionary of Wales (1849), pp. 25-52. URL: http://www.british-history.ac.uk/report.asp?compid=47797.

"In this county, where the rearing of cattle is in most cases the
farmer's principal object, and the dairy is almost entirely neglected, the
calves are not weaned until they arrive at double the age at which they are
generally weaned in other counties. This partly accounts for the bull-like
appearance of the oxen about the head and dewlap; but it is a received opinion
that they are hardier in consequence, and may be kept on coarser pasture. The
characteristics of the choice Anglesey oxen, commonly called Runts from their
small size and peculiar appearance, are (says the Rev. W. Davies, in his View of
the Agriculture of North Wales) the same in most points with those of the Roman
oxen described by Columella. Their colour is coal-black, with white appendages;
they have remarkably broad ribs, high and wide hips, deep chest, large dewlap,
flat face, and long horns turning upwards: their average weight, when fat, at
three or four years old, is from eight to eleven score lb. per quarter. These
deep-chested and short-legged oxen are much esteemed by the graziers for their
aptness to fatten; but they are not quite so well adapted for
draught."

Unfortunately, I don't know who Davies was, sorry.