Jadis was evil but she wasn't stupid
Jadis was evil but she wasn't stupid. As queen of nothingness she not only would not receive tribute but she wouldn't have anyone to defend her borders.
The following seems to be implied, but I have a hard time on this question drawing a line in the sand between my imagination and my observation:
First off, she provided food for the populace from her royal storehouses, something within her powers certainly and something which, to herself, seemed to justify her "right" to rule. Chances are the food was simple and not very appealing. Her approach to the garden party, turning the animals into stone for gluttony and waste as well as claiming to see Father Christmas indicates to me that she controlled Narnia through controlling access to food and drink. A very effective means, by the way, for in the Old Testament we see Pharoah with his storehouses of grain buying up personal soverignty over all the private property in Egypt during the seven years of drought....
Second, why is it always winter and never Christmas? She had the unmitigated gall to try and defeat Aslan but even she knew she couldn't win against the Emperor across the sea. So she took the time to learn the deep magic and try to use it in ways the author never intended, much as the crooked lawyer that insured a set of thousand dollar cigars, smoked them, and then claimed they were destroyed in a series of small fires (he won that one, by the way). In Narnia there is a certain magic associated with the renewal of spring and with Christmas. The only way Jadis could prevent her powers from being destroyed from beneath was to prevent winter from ending and prevent Christmas from coming.
Third, and perhaps most intriguing, is why Jadis and why then? She came in at the beginning and she was, in a sense, the Emperor's hangman. But queen? There has always been a human king of Narnia, methinks. Several things in the book suggest it. In particular I believe that the male heir to the throne was brought someone of Aslan's own choosing. This line of King Frank I, which I call the Angalandrian (Angle-Land) dynasty ended abruptly with the death of the last King without an heir. At the time the distant relatives in Archenland were arguing over who should go be the next King of Narnia, and unfortunately most of them wanted thereby to annex Narnia in an Empire to lay claim to its rich natural resources and open spaces. This foolishness, not typical of them, blinded them long enough to allow Jadis to act. First she pitted the different heirs against one another, and perhaps she caused the friction in the first place. Then she herself grabbed power, claiming to be human when in fact she was Charnian. This happened during the winter, and to prevent the spells she used in her conquest from being broken by the coming of the vernal equinox, she rebuked time and in doing so it was perpetually Hibernis 22nd. That's why it was never Christmas, because the same date kept repeating.
Not all canon, but I hope you found it interesting.