First, I would say ''all of a sudden'' :) you need the ''a''.
You can say ''I miss the snow all of a sudden'' although, without any context it seems a bit strange.
I wouldn't say ''I miss the snow out of the blue'' because…well again, it seems very strange.
''Out of the blue'' as the idea of ''out of no where'' ''without any expectations''
As ''All of a sudden'' only suggests that ''suddenly'' something happens.
1. All of a sudden, I realized I miss the snow
2. It started snowing all of a sudden
1. It started snowing out of the blue, in the middle of July
2. She called me totally out of the blue
If you have any questions let me know! :D