From what I've read and can happen, it's not something I would do, but if you really want to, I would weigh some wood similar to what you'd be hauling. Scale it up if needed. A load of wood can get pretty heavy in a hurry. All that weight out back is not good for a number of reasons, and the immediate one of concern would be tongue weight.
I don't know about firewood restrictions between states. Not sure if it's more restrictive than crossing the Canada/US border. You are allowed to go either way across the border with firewood as long as it is mill ends (sawn pieces of scrap 2x4s and 2x6s). Regular split firewood would result in a trip to Guantanamo Bay. We buy already cut mill ends from a pallet recycling place in Wa. and it's pretty inexpensive at $50 for an 8' pickup bed full of it and tightly packed.