Fred has the same problem! Just with socks though. We have a mat in the kitchen and he'll run around the house dragging socks and collecting them in the middle of the mat in the kitchen. When I get back from work, I walk in the garage door and see him laying there surrounded by all our socks!
I'm not sure if this is a bad habit or a cute one!
Sometimes when he drags the sock, it's longer than he is so he'll find a way to grab it and run and not trip over it. Usually he pulls it sideways!