I have three dogs. They weigh 14, 55 and 75 pounds respectively. I backpack will all of them ( but only one at a time). All three of them have different preferences.
The little one always hops in the hammock with me. She really like the opening on my No Sniveler. She sleeps on top of me and pokes her nose out the head opening.
The 55 pound dog has a short coat. When it's above 40 degrees or so, she sleeps under my hammock on my sit pad with my pack as a pillow. When it gets cooler, she too hops in the hammock. At 55 pounds, she is NOT going to sleep on my lap. I just move off to the side and try not to shift too much. She leaves her nose outside my OQ. (Terribly considerate of her not to wet out my down with doggie condensation.)
My 75 pound dog is a husky-shepherd mix. The only time I have seen her not panting is when it gets below 20 degrees. She just sleeps on my sit pad like the 55 pound dog. She's been in the hammock, but I think it's too hot for her. ( Although she probably would add 50 degrees of insulation to my hammock.)
I always have a tarp set up, and they all know when I get in the hammock it's bed time. If I'm not carrying a tent and setting one up for me, the dogs aren't getting one either. If you get them used to a pet tent or some special set up, be prepared to dole that out very time. Else, they will be out of their element. I would hate to be cold and tired enough where I can barely get my gear set up while still needing to pitch a pet tent. My dogs were all antsy the first couple of times I took them out. Basically, they became comfortable when they sensed I was comfortable. If you're antsy or stir often while you sleep, they feed off of that and respond in kind.
As we can all see, it's a matter of preference and there will probably never be a consensus. All of our dogs are different... we just do whatever makes them comfortable.
I take my dog along with me bc my wife will not feed it while I am gone. She sleeps in the hammock with me in my sleeping bag to help keep my feet warm. It helps that she is a sub 15# dachshund.
I don't have a dog now, but what about a separate hammock tied to the same head tree as yours? I know people use that setup sometimes for spouses or kids. Seems like it would let you stay in contact with the dog and keep him warm and dry without driving you bonkers.
will he sleep in those boot things? otherwise I am thinking the claws and the ripstop will come to grief..