I'm new to BYC but when I found your post I read it clear through, it brought back SOOO many memories of our Great Pyr - Moa. We bought her at 13 months old, still a pup but VERY large! You should go to
http://www.greatpyr.com/ to learn about the dogs you have. They give great insight to the the Pyr's nature and the best way to "train" them.
IMO you need to establish who is alpha dog very soon. I learned some tricks off the pyr site, like when Moa was chasing my drake and stepping on him trying to get him to fly. I was hysterical to say the least - my only drake!! I got her by the collar and made her lay down until I was ready to let her up. I stepped on her collar to keep her in the "down" position, and really chewed her out!! I kept her down until I felt better. Even tho she looked at me with those great... big... dark... eyes... She doesn't chase the ducks anymore to make them fly. She is now almost 2-1/2 years old full grown and 106 pounds.
I agree that the chicken wasn't wet from snow - it was pyr slobber. Moa used to do that as well. Never hurt them, just licked them and loved on them.
Pyr are by nature wanting to protect, they just need to learn who and what belongs and what doesn't. They were used to guard sheep without human intervention. So when she has to deal with humans, she has to learn where they belong too. Make sure YOU are on top - alpha dog. I remember one day when she was acting up I put her in the empty chicken coop for her "time out" away from the other animals. It took an HOUR before she let ME out of the coop. No aggression towards me or anything. She didn't want to be alone and she didn't want to be punished either. She just sat her 106 pound butt in front of the door and I couldn't push, pull or outsmart her to get myself out of the coop. Just like a kid, if I'd have let her have her way, I'd be 2nd dog, not top dog. An hour later she gave in and I got out and she stayed in.
We spent MANY hours walking the perimeter of the fence inside and out. I ALWAYS went through gates first, she always followed me. etc etc. If she pushed me out of the way to get through the gate, we'd stop and go back through the gate again and again until she let me go first. You get the idea.
Just the other day my DH watched Moa watch the ground, and take one big swoop in the dirt - she caught and swallowed whole, a ground squirrel. Moa has 1-1/2 acres of fenced pasture to play in; she lives there with 200 chickens, 11 ducks, 2 rabbits and 3 sheep. There are no longer any groundhogs, skunks, possum, squirrels, deer, coyotes, or woodpeckers in that pasture - just the critters that belong. Okay, I did see one mouse a couple of weeks ago.
Don't give up on your pyrs just keep working and working with them. When they finally figure it out. They are THE BEST. You can get ideas on the web site about keeping them from jumping up. Believe me you don't want a dog that big jumping up on you! Moa gives you "the paw" when she likes you or wants to play, everyone that I know who has a pyr their dog does that.
Fencing is a BIG issue. You will need a good fence to keep them in. They are, after all, following their instincts and expanding their territory so they can protect their "flock". If Moa gets out of the fence, she walks into town. She doesn't run, just walks about 6 feet in front of you, far enough you can't even think about catching her. When she's done looking around, she'll stop and lay down in your path and let you grab her by the collar and lead her home. FRUSTRATING to say the least, but that tells us she needs more exercise at home and we start playing the pyr version of fetch or something like that.
Pyrs aren't like any other dog. Learn all you can about THE BREED and how to deal with that, it'll be easier on both of you!!