Will frozen (frosted) garlic cloves still grow?

We harvested and "cured" (hanging in warm, airy attic space) our garlic in late July or August, can't remember now. Then my mother in law braided the heads and they got hung on our (open air) porch. I still need to plant them.

Last week we got our first frost, and over the weekend the temperature fell enough one night that a crust of ice formed over water in buckets-- maybe it was -2°C.

I'm going to plant next week (it will also be warmer, and isn't forecast to fall below freezing for the next 10 days), but is the garlic still fine to plant?

I guess if it over-winters in frozen ground, a few degrees below freezing in open air won't hurt it?

The chill probably did them some good.
Typically garlic is planted in the fall. The cloves will send out some roots and leaves, then growth slows as the weather cools.
The plants need a frost to initiate division of the clove into several cloves to form a bulb.
Here in north Florida I've had winters with only a couple of light frosts. Garlic has failed to divide in mild winters. I've learned to put them in the fridge and freezer for a couple weeks before planting.

We plant garlic in the fall in Manitoba and it freezes. It germinates every year without fail so I'd say you're okay. I know this is a little late but I figured I'd let you know what I've experienced.

Yes. Hardneck garlic even prefers that. Softneck garlic likes it to but no as much.
http://www.jubileeproduce.com/difference-between-softneck-and-hardneck-garlic/