Escape to the Wind

Escape to the Wind by Jennifer DiMarco
1993, Paperback

First book of The Wind Trilogy.
Tyger.  Part woman, part Beast.  Leader of the Windriders.  Together they struggle to survive in a post-Armageddon world where exposure to the fatal breath of the radiation-filled gales known as the Wind metamorphoses the body and soul.  New Seattle, the Windrider's home, is ruled by a military dictatorship called the Patriarchy; it is one of the domed cities where the world's scarce population is clustered, urgently seeking to multiply.
Tyger.  Warrior.  Double agent.  Murderer.  Lover of women.  When she decides to rebel against the Patriarchy, there is only one way out and into freedom.  Escape to the Wind.