I shall not be going to the theatre _____.

This is a first conditional sentence expressing a real future possibility. The structure is: 'If + present simple, will/shall + base verb'. The main clause uses 'shall not be going', so the if-clause must use the present simple form. 'It snows' is the correct present simple form for the third person singular. Hence, 'if it snows' correctly completes the conditional sentence.