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: 

HERMIONE.
What wisdom stirs amongst you? Come, sir, now
I am for you again: pray you sit by us,
And tell's a tale.

MAMILLIUS.
Merry or sad shall't be?

HERMIONE.
As merry as you will.

MAMILLIUS.
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!

How is the title related to the play The Winter's Tale?

Perhaps the answer to your question can be found in Act II, scene 1.  Herminone and her ladies are with the young Mamillius.  Herminone asks for a story.  Mamillius asks her if it should be merry or sad.  His mother requests a merry tale to which the young child replies"A sad tale's best for winter..."

Not only does this tell us that it is winter time in Sicily but it also foreshadows the first three acts of the play which makes the play appear to be a tragedy.  Winter symbolizes death and there is physical, spiritual, emotional death in the first three acts.

I believe that Shakespeare was experimenting with structure here, thus, the broken back structure of the play.

Just as the sun rises in the east and sets in the west, spring is born out of the death of winter.  This is exactly what we find in the Shakespeare's play.

The title reminds us of this, winter is always just down the road but spring isn't far behind.

How is the title related to the play The Winter's Tale?

This play deals largely with the pastoral, which in Shakespeare's time was idealized as perfect, carefree, and an ideal way of life.  However, the pastoral depicted in this play has a darker side.  Not everything is "ideal" in the lives of the characters...for instance, a terrible storm threatens the safe arrival in Bohemia, once there, Antigonus is chased  and eaten by a bear, and there are angry outbursts from characters which indicates that not all is well in paradise.

Perhaps we can take from this "other side of the coin" interpretation of pastoral life that the title comes to indicate that there are opposites to everything.  Pastoral life is usually portrayed in the spring and summer months where people are more carefree and joyful...the weather is warm, love is in the air, food is plentiful, birds are singing, blah, blah, blah.  The opposite, however, is true in winter.  The cold puts a damper on people's mood, food is not growing--and, unless people worked hard and stored food for the winter months, it is not plentiful--birds have flown south, etc.

The title, then, may just be showing that to everything and everyone there is an opposite, another side, a different mood, a darker more foreboding perspective.

Hope this helps!  Good Luck