Howdy Jack, you may consider an alternative. I've got the same problem as you, except it's the heat in the summer
I'm in Houston (Spring actually) TX. I thought about borrowing off the duct-work of the existing a/c to the house, (my shop is my 2 car garage, but I refer to it as "shop" LOL), but I didn't, because the duct system already seemed mis-applied from when the house was built. (I met my now wife 4 yrs after she had this house built) This would just take the air from other rooms, not to mention the return-air system. (I worked in the HVAC wholesale biz for about 25 years, I know what I'm talking about!!) The more return-air the better, but NOT with lathe, wood, finishing products, dust, fumes, etc!!! Plus, unless you want a divorce, don't do it!!
This is what I did, dunno if it'll work for you. I have a standard 2 car garage SHOP!! Home Depot has some insulation boards, I think they're designed for your attic, but they are 4'x8' kinda like ductboard,1" thick, but it's more like styrofoam material, it's a vinyl sheet on one side and a foil finish on the other side. On the garage door, on the inside panels, I just sized 'em and cut them with a razor knife, (2 per panel) foil side facing out & the inner foil side facing in!!! Then I taped each panel, where the steel meets the insulation with the foil tape (pain in the butt, but oh, well) anyway, squeegie it tight. Don't know if you have exposed studs like me, (I've used the exposed studs to add shelves!!) well, I hope this helps you!!!
good luck,
Ronnie