To cold pig something

The meaning that sponsored your grandmother's use is noted for 'cold pig' as a "technical term" among merchants in Manchester in the first decades of the 1800s. This appears in the 1833 Gimcrackiana, or, Fugitive Pieces on Manchester Men and Manners Ten Years Ago:

A technical term for goods returned, as being damaged or disapproved.

The note pertains to these lines of verse:

And, oh! may no cold pig, unwelcome sight,
Nor return'd wrappers e'er the sense affright!

In keeping with the season, I also reproduce here the vignette epigraph from the title page of that volume, along with its ascription:

The hallowed season and the joyful time
In which I used to greet you all with rhyme,
Is now return'd.

Oxford Sausage

Without belaboring the point, I observe that the work is dedicated "To the thrifty sons of trade, 'Manchester Men,' and the public".

A slightly different mercantile sense is recorded in Wright's 1898 English Dialect Dictionary:

goods remaining on hand unsold or returned.

Further corroboration from the early 19th century is in the 1823 Slang. A Dictionary of the Turf, the Ring, the Chase, the Pit, ...:

Pig...'Cold pig;' goods returned upon a tradesmen's hands instead of money, is an unsavoury thing, and so is cold pig.

Are you or your grandmother from Australia or New Zealand?

Green's Dictionary of Slang provides a few senses of cold pig, but the one that seems most similar to the meaning expressed in the question is noted as possibly derived from Tailor's jargon, and specific to Australia or New Zealand.

cold pigging (n.) [? tailors’ j. cold pig: a suit that has been ordered but not paid for or collected; such garments, possibly after alteration, would be sold off at a reduced price]

(Aus./N.Z.) hawking goods from door to door.

This sense, which dates back to 1900 and has attestations as recent as 2003, is distinct from a separate meaning referring to pouring cold water on someone or tearing off their bed sheets, as mentioned in a comment by Dan Bron, which derives from nautical slang:

nautical jargon cold norwester, a bucket of seawater poured over a new recruit as an initiation ceremony

So if you or your grandmother are from Australia, the tailors' jargon meaning adopted as Australian slang seems like a more likely explanation of the phrase than the other meaning.

However, the definition provided in this context still does not fit with exact precision, so if your grandmother has no connections with Australian lingo, the meaning could have deviated from one of the other slang senses into a narrower term confined to one region or subculture.

The term 'Cold Pig' is used in the John Lewis Partnership to this day, referring to a hand-written price ticket for an item of furniture that has been reduced in price because it is an ex-display item which is upholstered in a fabric that the customer can choose for themselves. An ex-display item like this needs a hand-typed ticket because of the huge choice of fabrics that it may be covered in. I was told the term 'Cold Pig' ticket means a bespoke item that has been used for display purposes and is being sold off.

Here is a screenshot of the ticket system form you have to select from. The Cold Pig ticket is also used for fabric remnants, and ex-display lengths used for window or internal displays etc.
This sounds like our use of this term is derived from the Tailoring term for a bespoke suit no longer needed by the customer perhaps.

I work in the window furnishings department of a fabric and manchester store in Australia. We use the term cold pig to refer specifically to custom made blinds, curtains or tracks that were either made to the incorrect size by the manufacturer or were damaged in transport. These products are then sold as a cold pigs for under $50 with no returns or exchanges.