But the Martins occupied her thoughts a good deal; 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… (Chapter 4)

Interesting suggestion and article too—thank you, I quite enjoyed it. I wonder how far Harriet’s interest in the cows went—did she play at or even help in some small way or did she just gaze at them longingly? (;D) Either way, I think there might be something of playing pastoral and perhaps also of playing house in Harriet’s feelings because she seems to me quite overcome with enthusiasm for the pleasures and the people at Abbey-Mill Farm. IMO Harriet was impressed by their style of living and well aware of Mr. Martin’s attention to her and it seems to me so is his mother:

Mrs. Martin had told her one day, (and there was a blush as she said it,) that it was impossible for any body to be a better son; and therefore she was sure whenever he married he would make a good husband. Not that she wanted him to marry. She was in no hurry at all. (Chapter 4)

I think Mrs. Martin does wish for her son to marry, perhaps not in a hurry but maybe she approves of her sons choice, wants to forward his happiness and is attempting to help him along. Perhaps suggesting the pretty little Welsh cow be called Harriet’s is a way of drawing her into their family circle.

"And when she had come away, Mrs. Martin was so very kind as to send Mrs. Goddard a beautiful goose: the finest goose Mrs. Goddard had ever seen. Mrs. Goddard had dressed it on a Sunday, and asked all the three teachers, Miss Nash, and Miss Prince, and Miss Richardson, to sup with her." (Chapter 4)