I have grays in my area as well. They also do not seem to target my birds even prior to having new dog in place. They seem inclined to stay more in the woods where my chickens at present do not venture. For me I see more grays in or near town, especially along roadways with dense groves of...
For above subdiscussion see following link. http://www.cougarnet.org/northeast.html
Photo provided by OP looks like a fox, mostly likely red. Feet to gracile to be a cougar. Long and bushy tail is evident curling away to left side of animal pointing away from camera.