Is it against code to have a dryer vent into a Garage?
As always, check local
Into a garage is normally always frowned upon, through a garage can normally be done....but, sometimes a cool/cold garage can cause the moist air to condensate and sweat allowing lint to collect inside the vent. Wrapped vent pipe might be a good idea.
is join the exhaust with the only exterior duct work in the garage that brings in outside air for the heater and just not run the heat with the dryer in the winter.
Vents should always be seperate and not joined together.