What you would need is 20 strong rectangle containers which you tilted at 5 degrees for the first layer, then tilt more and more to get the curve of the walls. If you build it in sub zero temperatures the blocks should melt at the bond and refreeze fairly rapidly.
The last few blocks need to be hand shaped to finish the arch off well, and it needs to be accurate as this is where the igloo gets its strength.
On the other hand I wonder if you could not get a weather balloon or arch shaped inflatable and spray a mist of water on it which would build up layer upon layer of ice put some fibers in there for extra strength. Deflate the infallible and drag it through the door.