It really depends on if there's a lot of shrub-height ground cover or not. Tall trees like pines make great places for hawks to hide while planning a swoop.
I've got a big problem with tall trees around my property. The forest hawks like goshawks are very clever at winging through the trees without being seen, and then they divebomb without warning. I've lost big adult birds.
So I would say a forest helps some aerial predators like goshawks...
If you could plant a lot of low shrubs the chickens would have a much better chance.