Yes, I actually thought about that as well; what I call an old beater truck because you don't care if you put a few dings in it because its main purpose is a work truck.
I agree on a trailer, just watch out how heavy the total weight of load and trailer. Your going to strain the transmission on a vehicle not really designed to tow. Stay within the manufacturer tow ratings. One for safety but two so you don't burn up the transmission. It will tow way more than it's rated for...untill it won't.
Harbor freight has light duty trailers that are good for small wood hauls. There light duty but a good price for what they are. Will keep the weight of the trailer down as well. Or you can get one of those ultra light trailers at Tractor supply company on black friday. There for like atv or lawnmower is all. Just a single square tube for the tongue connected with 2 bolts and mesh floor. They usually are in sale for $500.