I was wondering why my damper on my wood furnace only open when the blower is on? When the blower shuts off the damper closes! Should it not be the other way around?

It depends on what damper your talking about. If the wood burner is tied in with different central heat and air duct work, it will have a back flow damper to keep the air from going in a circle. You should have two in your system to isolate each. If the damper is in your duct work yes it is normal.