This is a very interesting question to consider, because many argue that the ending of this play represents the complete oppositie of freedom with the way that Katharina submits to her state of being a wife, dependent on her husband for everything. However, it is possible to argue that Katharina finds a true freedom in this role that allows her to accept her new status as a wife, whereas before what made her so unhappy was her unwillingness to accept her position in society as a well-to-do unmarried daughter. Note what she says about being a wife in her final speech in Act V scene 2:
I am ashamed that women are so simple
To offer war where they should kneel for peace,
Or seek for rule, supremacy and sway
Where they are bound to serve, love, and obey.
As unpalatable as this ending may be to 21st century audiences, it is certain that Katharina finds a measure of happiness in embracing her new role as a wife, even if she may not fully like it. In the end, although Katharina offered the possibility of a woman who determined to be her own mistress, the ending strongly suggests that social roles are permanent and cannot be challenged forever, and that those characters who accept them actually end up happiest. Although Katharina has to accept her husband's lordship over her, she does at least end up being part of society rather than having the forces of society ranged against her, and because of that, she gains some measure of freedom.