You will need:
-lots of wet snow
Note that this requires very wet snow, especially for the cannon.
The wetter the snow is, the easier it will be to get the protuding mouth of the cannon to stick.
If your snow isn't wet enough, you can just support the entire barrel on a block of snow.
Also I wasn't planning for this to be an instructable so I didn't take pictures of every step.
I just made some 3D models in Blender. Because my computer was having issues, they didn't turn out exactly as planned, but they should still give a general idea of what's going on.
Step 1: Create the cannon base
Turn the sphere into a rectangular prism.
The dimensions should be about 1 foot by 2 feet by 1 foot.