This would be a very long, indeed thesis-length, argument to make in full. But I think one of the many, many ways of interpreting this fascinating late Shakespeare play would be to argue that the play charts the thawing of cold, harsh winter into spring and into rebirth. Spring, of course, is the time when new things are born.
Leontes' cold, murderous jealousy gives way - as the play progresses - to forgiveness, and a new lease of life. And, of course, the queen is "reborn" from the dead.
The first half of the play marks coldness, icyness, and the death of the prince and the supposed death of Hermione: as Mamillus says "a sad tale's best for winter" (2.1.25). And then, in the second half, Leontes calls his penance in the second half of the play his "recreation". Autolycus announces the shift into the second part with a song about spring:
When daffodils begin to peer,
With heigh! the doxy over the dale,
Why, then comes in the sweet o' the year;
For the red blood reigns in the winter's pale."
As the old shepherd says, marking the play's shift into happiness and merriment: "Thou met'st with things dying, / I with things new born" (3.3.112-13).
The saving nature of birth is everywhere in the play: when the messengers return from the Delphic oracle, wishing that "something rare / Even then will rush to knowledge... And gracious be the issue" (3.1.20-22), even knowledge becomes something that might be born in order to save the day.