Well, it depends what you mean. Shakespeare's voice as a writer is everywhere in the play, as it's all written by him: so the mode of expression he personally employed to write lines of dialogue for characters is shown in every single one of the lines.
If you're looking for clues to Shakespeare's biography, that's somewhat more difficult to find: because we don't know a great deal of concrete information about Shakespeare's life. The transforming beauty and magical power of the forest might be read as stemming from Shakespeare's childhood spent near the Forest of Arden (a real forest in England which appears in "As You Like It").
Some scholars have also seen Oberon's reference to an "imperial votaress" in Act 2, Scene 1, as a coded reference to Elizabeth I, who might well have been in the audience for the play. The idea of the magic flower 'love-in-idleness' and falling in love (read - marriage?) instantly might also be read as a comment on Elizabeth's status as the 'Virgin Queen', and her insistence on remaining unmarried that attracted much controversy in the later years of her reign.
We know that Shakespeare later wrote topically about Elizabeth I in "Richard II", but can we hear a political Shakespeare's voice in "A Midsummer Night's Dream"? There's no definitive answer: it all depends how you read it.
Shakespeare was first and foremost a playwright. The scenes when the rehearsal and the staging of the play "Pyramus and Thisby" take place contain Shakespeare's opinions and insights into contremporary stage and theatre craft. A few examples are as follows:
1. "Let it (the prologue) be written in eight and eight." ActIII sc1.
2. Bottom loses the chance of earning six pence for playing his part in the play, ActIV sc2.
3. "To show our simple skill/That is the true beginning of our end." Act V sc.1.