Warning: this post is technical and pedantic.
Two years ago I wrote a post about the evolution of Canada’s coat of arms. Prior to Confederation in 1867, though, it seems that no colony regularly used a coat of arms. Instead, colonies represented themselves with emblematic seals, on the rare occasions when they needed to. Few people know about these seals nowadays; it seems that joining Confederation and adopting a coat of arms went hand-in-hand.
One place where you can see some colonial-era seals is in the Parliament buildings in Ottawa, near the entrance to the House of Commons. I took these pictures in 2006, but I only noticed just now that they aren’t exactly parallel to each other.

Upper Canada (i.e. Ontario).

Lower Canada (i.e. Quebec).

New Brunswick.

Nova Scotia.
You will notice that the seals of both New Brunswick and Nova Scotia have renditions of the royal arms hanging over an emblematic scene, a feature that does not exist in the seals of Upper and Lower Canada. This wasn’t always the case, however: Conrad Swan’s Symbols of Sovereignty (1977) illustrates colonial-era seals for both New Brunswick and Nova Scotia that are simply the emblematic scenes.

“Obverse (proof impression) and reverse of the 1817 Great Seal Deputed of New Brunswick of George III.” From Swan, Symbols of Sovereignty, 150.

“Great Seal Deputed of Nova Scotia of George III, in use from 1818.” From Swan, Symbols of Sovereignty, 128.
Or rather, what we have here are double-sided seals, with the emblematic scene on one side, and the royal arms on the other. There was a time when official instruments featured seals hanging by ribbons from the bottom of the document, in which case it was possible for a different design to be impressed on either side of the wax. Letters Patent originating from the College of Arms in London are still done this way, as is the honorary grant of arms to the Virginia Senate:

What seems to have happened, over the course of the early nineteenth century, is that dependent seals went out of fashion, and seals impressed directly into the document became more common. Thus, the royal arms had to migrate from one side of the seal to the other, so that both the arms and the scene could appear on the same side. This shift occurred in Upper and Lower Canada as well:

“Proof impression of the Great Seal Deputed of Upper Canada of Victoria.” From Swan, Symbols of Sovereignty, 167.

“Proof impression of the Great Seal Deputed of Lower Canada of William IV, 1832.” From Swan, Symbols of Sovereignty, 111.
Note the dates here: the first is from the reign of Queen Victoria (1837-1901), and the second from the reign of King William IV (1830-37), while the double-sided ones are all from the reign of George III (1760-1820).
Actually, the seal of Upper Canada for Victoria could not have seen much use, because in 1841 Upper and Lower Canada were united to form the United Province of Canada (subdivided into “Canada West” and “Canada East,” but still one polity). The seal of the United Province of Canada showed both seals of Upper and Lower Canada together, under the royal arms, as had become the custom by that time.

A. & P. Vachon Collection, Canadian Museum of History.
So I would say that the display in the House of Commons could have been done slightly better. It should either show four emblematic scenes alone, for Upper Canada, Lower Canada, New Brunswick, and Nova Scotia – or it should show only three seals with the royal arms over the emblematic scene: Nova Scotia, New Brunswick, and United Canada, as representing the political situation on the eve of Confederation. (People forget that only three colonies came together in 1867, because immediately Canada was redivided into Ontario and Quebec.)
But as I say, each of these now-provinces has a coat of arms, and that’s what people know. These coats of arms are what got engraved into the provincial seals. From Wikipedia, here is Ontario’s:

The royal arms appear in the centre, while Ontario’s arms are at the base, both of them within a glorious Victorian-Gothic frame.
Apparently this was a template: other provinces have the same design. Quebec certainly did:

From Swan, Symbols of Sovereignty, 114.
Swan designates this as the “Present Great Seal of Quebec” but the design did not last very long after his book was published in 1977. The previous year, you see, the Parti Québécois had taken power in Quebec, and proceeded to refashion it in their image. From Wikipedia, here is the real present seal of Quebec, which dates from 1979:

So they jettisoned both the royal arms and their provincial arms, which features references to Britain and Canada as well as France. (Frankly, I’m surprised that they haven’t changed this as well.)

Wikipedia.
Instead, the current seal just features a simple fleur de lys, done in the standardized Quebec style (and a ring of fleur de lys around the exterior, like the hem of the old Quebec Nordiques sweaters). You’ll also note an acute accent over the first “e” in Quebec, even though accents are optional on capital letters – and no reference at all to Quebec being a “province.”
Vive le Québec libre!