They are similar phrases but with slight differences. All of a sudden - focuses on the time something occurred. It means suddenly and unexpectedly. I was riding my horse and, all of a sudden, he spooked for no reason. Out of the blue - focuses on the unexpected arrival of something. I was riding my horse and, out of the blue, a snake dropped in my lap.

Hi! Interesting question! 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. Example sentences: 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 byebye