Refrigeration

[sovereign1]

I've been looking into living a self sustaining life growing my own crops, etc.

Is a hole in the ground good for refrigeration purposes?

If so, how deep and what would it be ideal for?

[Eeyore]

Interesting question, it would work for storing root crops in the winter months and for keeping some things cool in the summer. However I don't think you'll find it keeps certain things frozen or at a cold enough temperature to be safe for eating.
You might want to look up some information on "root cellars".