"Independent as a pig on ice."

Elizabeth Fais has a blog post titled "Confounding Colloquialisms: Expressions that make you go, 'What?'" in which she discusses the phrase:

“As Independent as a Hog on Ice” Flailing About

Strangely enough, I’m not the only one who has been confused by this saying. This phrase has been baffling people for decades. Yes, decades! Etymologists started searching for an explanation from the time it first appeared in the mid 19th century. In 1948 Charles Earle Funk titled his first book of word origins “A Hog on Ice”. His foreword contains a seven (7!) page narrative of his inconclusive quest for the roots of this phrase.

The Oxford English Dictionary defines the phrase as “denoting independence, awkwardness, or insecurity.” That about sums it up for a hog that’s slip-n-sliding across the ice, much like Thumper and Bambi in the Disney animated feature. “You’re doing it your way, and making a mess of it,” was what my father meant by his independent-as-a-hog-on-ice speech.

Time magazine usage in 1948, “They like to think of themselves as independents . . . independent as a hog on ice.”

The Free Dictionary claims that it originates from curling, but based on the description of the "inconclusive quest" conducted by Charles Earle Funk, I am highly skeptical of that claim.

Was your wife's maternal grandmother from New England, perhaps?

The earliest reference to "independent as a hog on ice" that I've found comes from Short Patent Sermons (1841), in a sermon entitled "On the Increase of Nominal Saints". The book is by Dow, Jr - allegedly a nom de plume of Elbridge G Paige This is introduced by a quote from Dryden:

Truth is, our land with saints is so run o'er,
And every age produces such a store,
That now there's a need of two New Englands more

Anyway, back to the quote itself:

No wonder Dryden thought there should be two New Englands more when he saw how much hypocrisy there was in the world. What would he think now, if he was alive? But New England, at the present day, isn't what it was when my father was a boy. Then it was the home of uprightness - the people were all as honest as the cooper's cow - independent as a hog on ice - sober as judges - and moral as a quantity of psalm books.

While this answer doesn't explain the origin of the term, it establishes its existence 177 years ago.

There is further indication of the usage of this term on July 1st 1904, in this ghastly (IMHO) article on Filipino independence, published in the Weymouth Gazette, quoting the Manila Times. This usage does show an indication that a "hog on ice" is considered to be uncontrollably independent, and in need of some herding in order to move it in the right direction.

Freedom - or independence, as the native minds like to style it - is indeed the crying need of the native, but the kind of freedom that he requires is the spiritual freedom of which Milton wrote, and not the release from governmental tutelage, which, when considered in the light of his abillity to take care of himself, his country and its industries, would be as the proverbial independence of the "hog on ice." In the present stage of his development the Filipino needs the strong supporting hand of the Aryan race to lead him in the paths of industrial progress and intellectual attainment, and at the same time to support him lest he dash his foot against the stone that always waits for the foot of the unwary.