I never trained in the morning somewhere that got cold, but I did train in North Dakota during the winter in a garage with no insulation when the temperature outside was -60 with windchill, so take that for what it's worth.
Space heaters were helpful. I would say, upon waking, before doing anything else, run into your garage and turn them on so that they have a chance to start warming things up while you do whatever else you need to get ready.
Layers are a must. I wore some thermal base layer stuff for upper and lower body. Also, you'll want a knit cap/beanie.
I never wore gloves or anything. Your hands will adapt to the cold steel, and worse comes to worse, you can heat them up on the heat dish between sets/right before attempts.
EDIT: Oh yeah, and don't be afraid to head back inside in between sets to warm-up as needed. I couldn't pull off this trick since I had 2 puppies that would go ballistic as soon as they saw me, but every once in a while I'd hang out in one of the cars in the garage.
In truth, you adapt/warm-up pretty quick. I'd have a lot of workouts where I stripped off all of my upper layers and was shirtless.