Much of the conflict in The Winter's Tale comes from the unchecked and absolute power of both Leontes and Polixenes, both kings and fathers. Their power is used in the manner of a tyrant, threatening both the happiness and the lives of the other characters.
Leontes's weaknesses as a human being permit him to use his power unwisely, even harmfully. When he becomes paranoid over whether or not his wife Hermione is having an affair with his best friend Polixenes, he starts using his power to take revenge on all of them. Leontes tries to have Polixenes killed and when Polixenes flees the country, and Leontes also has Hermione imprisoned. His attempt to have his own infant daughter killed proves the last straw; the messengers that consulted the Oracle of Delphi, who pronounced Hermione innocent, tells the king that he will lose everything and live without an heir "if that which is lost be not found."
Ultimately, Leontes's abuse of his power causes him to lose everything he once held dear. He is told his son and Hermione have died because of the emotional strain he put upon them. History almost repeats itself when Polixenes tries to prevent his son Florizel from marrying Perdita due to the assumed class difference between them. He even goes as far as to threaten to disfigure Perdita, evoking Hermione's earlier persecution. Indeed, women are the most vulnerable to unchecked power. The merest slander or accusation of misbehavior can mortally threaten a woman, such as when Paulina is accused of witchcraft.
Ultimately, truth and love save the day, but the unchecked abuse of power on the part of the two kings always keeps the action of The Winter's Tale on the edge of tragedy.