There are many ways in which depth is not related to physicality, or in other words there are many ways in which depth plays a part in life even though you may not be speaking of actual depth that can be perceived with the eyes. Sometimes depth has to do with the mind which is important and all too human. This is why it might show up in your dreams, because you are thinking big.
If you have a dream about a deep voice then this means that you feel a menacing presence in your life. Deep voices usually come from an area of fear or from a sense of fear that has been about you lately. If you hear a deep voice in your dreams it means that you feel pressed upon in real life as if someone is dogging you or getting on your nerves. This is always a possibility. If you have a dream in which you are the one with the deep voice it means that you feel like your masculinity is taking over and you feel a lot more in charge than you have been feeling lately up to this point. You feel like you have a lot more power and feel like you are in charge enough to control your own destiny. You are the big man on campus and you will not let anyone forget it because of how important the status title is to you. Likewise to dream of a deep breath means that you are having a very sexual dream probably because in real life you feel horny or like you need some physical contact from someone soon in order to fulfill you.