*****
I never have let any of my dogs ride around with their head's sticking out of the window if my speeds were above more than about 10-15 mph. When I start to accelerate, the back windows go the rest of the way up. I've had too much shit bounce off my windshield, mirrors or the arm I've got hanging out of my window to risk blinding my dog.
And no, I've never let a dog ride in my lap either, not even Legal Lucy. My dogs either rode on the passenger's side in an old style pickup, or in the back seat of a crew cab or passenger car.