If cold air comes into your laundry room through the dryer vent, you should be able to stop it fairly easily. The vent should have a flap (or flaps) at the end to stop air infiltration (see photos). Go outside and make sure there’s a flap and that it’s not stuck open. If the flap works well, check the caulking. If it’s cracking and peeling away, it’s probably allowing cold air to leak in. Cut away the old caulking, make sure the vent is flush against the siding, and apply new latex caulk.
If the flap doesn’t close on its own, try cleaning it and then spray silicone on the pivot point. If the flap still won’t close, replace it. A new vent costs about $5 at home centers, and installing it will only take about 15 minutes.
Start by cutting away the caulking around the vent on the siding with a utility knife, remove any screws and unclamp the duct leading to the dryer. Slide the old vent out of the wall, slip in the new one and reattach it to the duct. Caulk around the vent flange.