I don't know about the gnawing and hiding bit, but my own dog (a mini schnauzer) doesn't like throw pillows being in her way when she jumps on the sofa or into an easy chair for a nap. She routinely butts with her head throw pillows onto the floor so she can stretch out in comfort with no "obstructions." It's so funny (to me) when I walk into the living room and find several pillows scattered over the floor. It obviously doesn't take much to amuse me!
You don't say whether or not the pillows your dog is moving are small throw pillows (decorative) or the actual couch cushions. If the latter, especially since he's half Lab and some of them are major chewers (think Marley & Me), you may come home one day to find the sofa chewed to pieces. My granddaughter's Lab mix chewed up a large section of her mattress.