According to William J. Higginson's Haiku World, migrating hawks fall into autumn, but "hawk" by itself is a winter season word. "Falconry," along with "hunting," "deer hunting," and "tracking" are all winter season words as well.
I grew up watching hawks and have always enjoyed them. I am also a big fan of castles, and I've noticed there are usually plenty of hawks around the castles here. The romantic in me likes to think its because they remember the old days when they hunted with the samurai. The realistic side of me thinks it's more likely to be that castles are essentially parks with lots of trees and a moat, and so tree critters and fish to feed on.
Either way, they are beautiful birds.