I keep finding better and better ways to breach aquifers in freezing biomes, or, well, any biome with a winter. First I found out about the advanced freezing method, and now I just found out a way that's put me on track to breach a 7z deep aquifer with a 3x3 hole in a little over a season (I might need a drain down to the caverns if I want to make the last layer 3x3, but that's a future problem). No pumps involved, though you do need at least two stones to make grates from which is a problem if you're in a tundra, in which your aquifer is probably in dirt.
It goes like this:
1. I dig a 3x3 hole from the surface to the top layer of the aquifer, revealing it to the freezing weather.
2. I dig a channel on all of the tiles except the center tile. They will instantly freeze over to ice.
3. Up/down stair in the center tile. Ice != aquifer, so the stair won't be flooded.
4. From the new up/down stair, I channel the ice again. This makes a 2z hole with an ice floor over the top, each with their own layer of aquifer. The top layer drains into the bottom, where the water is prevented from freezing by the ice floor above it.
5. Place grates around the upper level of aquifer and smooth the sides.
6. Remove the grates, bring them to a safe spot (it's easy to lose them in the water if you're not careful with how you're removing them), and then channel out the floor of ice above.
7. The lower layer is now safe to dig into. Dig an up/down stair in that center tile and start from step 3.
8. For the final layer of your aquifer (which you'll be able to see because of the up/down stair) you cannot remove the ice around the stair because there's no lower layer for the water to flow into. Just skip everything else and dig another stair into your sweet aquifer free stone.