How might one justify the title of "The Winter's Tale"?
Actually, the title of "The Winter's Tale" is one of the few Shakespeare plays actually to contain a worked-in reference to its own title:
What wisdom stirs amongst you? Come, sir, now
I am for you again: pray you sit by us,
And tell's a tale.
Merry or sad shall't be?
As merry as you will.
A sad tale's best for winter. I have one
Of sprites and goblins.
It's interesting, isn't it, that Shakespeare locates his own play as a tale told by a young child - a bed-time story, and one that may be "merry or sad": of course, in the end, after taking a profound turn toward sad, Shakespeare's play ends up happy.
Yet there is another important childhood relationship in the play: Polixenes and Leontes
We were as twinn'd lambs that did frisk i' the sun
And bleat the one at th' other. What we chang'd
Was innocence for innocence; we knew not
The doctrine of ill-doing, nor dream'd
That any did.
Whose story is the "tale" then? Who is its teller (of course the play unlike "Pericles" has no fixed narrator!)? Is it a story about the loss of innocence (the death of Mamillus and the sadness, even at the very end of the play?)? Is it a story about a grown man, Leontes, regaining innocence in the revival of Hermione? You could read the "tale"ness of the "Winter's Tale" many ways. But that, at least, is the theme the title points to!