Ironglow: the nests you see are most likely made by the Gray Squirrel. The Red Squirrel or Fox Squirrel is also refered to as the Ground Squirrel and lives in ground nests and sometimes trees. They will occupy Gray Squirrel nests when the fleas drive the Squirrels out, especially from inside trees.
The Gray Squirrel is the most aggressive. The Red Squirrel seems to be the more aggressive but isn't. Sometimes Grays will kill the Reds. The Black Squirrel is a Canadsian transplant, as I understand, and are not as aggressive as the Gray Squirrel - this I have been told but I have seen a fair number of Black Squirrels in the neu yawk city area and particularly in the Bronx and only on the fenced grounds of the Bronx Psychiatric Center of all places. They must really like the nuts............................
I thought I had a pair of Black Squirrels in my yard a couple of years ago but couldn't really tell if they were black in color or just a very dark gray. Unfortunately, a Red Fox took them both and I wasn't able to verify what I saw.
I saw your other post about a squirrel dog and the types of breeds you are considering. I do not know anything about those breeds and cannot advise you there but if I was looking for a smaller dog - less than 35 lbs, smooth coat and a good house dog I would be tempted to check the local shelter or rescue groups for Poodles. The Standard Poodle will go to 50 - 95 lbs (depending on breed line and gender) and although large, they prefer laps and couchs if given the chance. The next size down goes to about 30 - 35 lbs and are great companions and do not shed (they have hair, not fur). And I have never seen a Poodle, regardless of the size, that won't tear right after a squirrel or any other furry little critter if given the chance. I think that no matter the breed you will have to train them to the gun and to the sound of gunfire although having a tasty Squirrel they can savage after you knock it out of the tree might help..........HTH. Mikey.