"Today," she says. "And it is quite a long way, so bring whatever companion you like, except for the core of my Guard, who I will need here, and ensure that you pack well for it. I would give you a few jelly beans to content you on your way, but you would only eat them all at once, so instead I will give you a large number when you come back, and that will have to do."
"There may be some writing around the garden," she adds, almost as an afterthought. "Don't trouble yourself about it. I have eaten one of the apples myself."
She smooths said hair and plants a chilly kiss on his forehead. "Go, prepare for your journey, and you will be back all the sooner, and be my eternal Winter."
He doesn't bring a companion; he does bring food that will last, and flasks for water, and a sword and a knife and a good coat. And the map. From all of the hunting he has done for his Queen, he knows little tricks like how to take shelter in the snow and which trees to trust with his business; he won't have any trouble crossing the country of Narnia.
After that, it may get interesting.
There are a great many mountains in his way, with hazardous slopes and even bitterer cold at the high altitudes.
But once they have been crossed, there is a garden.
At the second, he feels cold, when he first bites it - and colder as he goes on - and at the end of the apple he is so much so that "cold" has ceased to have meaning; he can no more feel cold than a snowflake can.
At the third apple, he may notice the color of his hands changing, as though he is a snowflake, or a human-shaped tracery of frost on the landscape.
And what happens is -
He laughs with delight, drags a handful of long curly hair in front of his face; the morning light ripples through it, glinting blue and white and green from the ice-black strands. He stretches out his arms and watches them shine with all the colours of frost.
"I'm Winter," he says gleefully, spinning around with his arms flung out, whirling and whirling until he sits dizzily at the base of the tree. He hugs it. It is a good tree and he loves it very much. He's not hungry anymore, not even a little bit, except for the familiar squirming ache when he thinks about jelly beans.
He doesn't get hungry again the whole way back to the castle.
He eats anyway, once or twice, and the rest of the time he doesn't; it doesn't seem to hurt him either way. He does get thirsty, but eating ice and snow solves that. He's stronger and faster, though not as strong as his queen; he tires more slowly, but he still needs to sleep.
He can curl up in a snowbank and it won't melt. Snow makes a nice blanket, when it's light and fluffy. He does that a lot.
A month and a half after he left, he arrives at the castle gate with snow in his hair and a bright beaming smile.
"My dear Eternal Winter," she purrs. "Whatever has happened to you? Tell me everything."
She laughs. "I told you to eat one apple, greedy child. Who knows what will come of this in the long run? But come here, sit by me, and I will give you some jellybeans, unless you no longer want them now that you have changed color and grown chilled."
She rearranges him according to some opaque whim and pats his cheek and conjures up a jar of jellybeans; it is the first full jar he's been allowed since she first collected him.
On one occasion, she produces a container of jellybeans not for him, but for Maugrim to distribute, because she is going to an island in the far North with some of her retinue - and not Winter - in the hopes of retrieving some arifacts and books that may have use for her. The jellybeans are to keep Winter "out of trouble" in her absence.
They are promptly distributed, and everyone who's received any - is, first of all, careful not to eat them, and, second, curious about the extent of how good they are at controlling Winter.