willows do need to be outside in the winter time. You can transplant almost anything right up until the ground freezes in the fall, after it goes dormant. I've transplanted things in Feb during a sudden thaw. It just wakes up somewhere else. Not everything will survive this, but lots will.
willows root very easily from cuttings. If you know of a pussy
willow somewhere that you can just take a few stems from, why not do that in the
spring. Just put them in water until they root and then transplant and keep damp until it starts
growing. I've grown several curly
willows this way and one huge weeping
willow. It's best to do this in the
spring.
You don't even have to root them in water first. I've started them just sticking the pieces in the ground and watering. It's the cheapest way to get
willow trees. Use several pieces to make sure you get some that grow.