Although it’s an old question, the answer to this seems to be left open. I was struck by the final quote, “Lo, like a Cheshire cat our court will grin.” Since Cheshire was a famous cheese producing region, surely they had a serious mouse problem. What makes a cat happier than a fat mouse? They aren’t physically grinning, but it helps make a snappier phrase. “Lo, like a Cheshire cat our court will be fat and happy?” Nah.
Shaping cheese into cat forms also makes sense if you believe that the mere sight of a cat could keep mice away. It would be kind of like a scarecrow that probabaly wouldn’t work that well.
Around these parts, it’s customary to include a link to the column in question, so that we’re all on the same page, so to speak. Sometimes a regular member will drop by to supply one; other times the moderator of the forum will drop by and deliver his canned reply:
[Arnold Winkelried]
Welcome to the SDMB, Rhesus, and thank thee for posting thy comment.
Please provide a link to Cecil’s column if it is on the Straight Dope website.
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Of course, mice aren’t really all that fond of cheese. Most rodents prefer seeds or other plant material, and I understand that they’re crazy for peanut butter. I would suspect that the cats would like the cheese better than the mice would. But that might not matter to the origin of the idea, so long as folks believed back then that mice love cheese.