From Alice Morse Earle's Colonial Days in Old New York (1896):
In Albany in 1677 all "Shrovetide misdemeanors were prohibited, viz.: riding at a goose, cat, hare, and ale." The fine was twenty-five guilders in sea-want. What the cat, hare, and ale part of the sport was, I do not know.
Feb., 1677. Proclamation was made prohibiting all misdemeanors which have often occurred here on Shrove Tuesday, viz,: riding at a goose, cat, hare and ale, &c., on a penalty of ƒ25 seawan.....Order of the court to prevent and punish severely the shameful violation of the sabbath especially committed by the inhabitants of Kinderhook, and the appointment or Jochem Lambertse deputy sheriff strictly to attend to it.
My question is simply: Can History StackExchange answer the question that Earle couldn't? What is the significance of "cat, hare, and ale, etc." in the context of Shrovetide entertainments?
My best guess is that it was supposed to parse as "riding at a (goose, cat, hare...) and (ale, etc.)," but I have no evidence that "riding at a cat" or "riding at a hare" was ever a thing.
UPDATE: I'm restoring the [alcohol] tag to this question, as I first ran across the Earle quotation in John Hull Brown's Early American Beverages (1966). Earle may have been totally mistaken in assuming that "cat, hare, and ale" was supposed to be parsed as a set phrase, which then "tricked" Brown into thinking it was relevant to his subject; but on the other hand, it's the "and ale" part that makes the quotation puzzling at all! If the proclamation had referred simply to
...misdemeanors which have often occurred here on Shrove Tuesday, viz,: riding at a goose, cat, hare, &c., on a penalty of...
then the meaning would have been totally obvious. "And ale" specifically is what's throwing me.