The turn-of-the-twentieth-century etiquette book Twentieth Century Culture and Deportment, or The Lady and Gentleman at Home and Abroad by Maude C. Cooke (Philadelphia: National Publishing Company, 1899) devoted part of a chapter on artistic home decorations to the "cozy corner". The construction and decoration was described in some detail:

Have your carpenter make a double right-angle bench, with a high, straight back. The seat must be two and a half feet wide, and the top of the back five feet from the floor. This now looks like an ungainly three-sided square, or rather oblong, for it is better to have one side somewhat longer than the others. The wood should be stained cherry or oak, to match the other furniture in the room, and oiled and polished so as to be smooth and of rich appearance; or, use hard wood, black walnut, ebony, mahogany.

The seat and inside back may be thickly and prettily upholstered, and then piled high with pillows, or, the wood having been nicely finished, the upholstery may cover the seat only. Be sure and have the seat made low, otherwise the Cozy Corner will be uncomfortable, its name will be belied, and no one will hie to what might have been the favorite seat in the room...

...The seats should be piled with sofa pillows, and in the inclosure a few hassocks would not be found amiss.

The purpose of the cozy corner?

The word cozy suggests warmth and pleasantry, as well as comfort. Therefore, this corner is always by the fire, and those occupying it are presumably cheery and happy.

It is just the place to rest in, just the place to read in, just the place for you and your dearest friend to chat in, just the place to play a game in, as bags, balls, etc., could easily be tossed from one seat to the other; just the place to lay plans in, for you are in no hurry to move, and so your plans, not being hurriedly completed, would be more apt to prove satisfactory; just the place to nap in, just the place to frolic in. Indeed, just the place to add to our already comfortable homes if we would have them one remove nearer the ideal home than they now are.

(quotes from pp. 479-80; the entire book may be found online at Project Gutenberg)

This being a dance history blog and not a nineteenth century home decor blog, one might wonder why exactly I find cozy corners worthy of attention. Oddly enough, at least in early twentieth century Maine, they seem to have sometimes formed part of the decorations at college dances...[actual cites behind the cut]