You will never hear anyone say darling, could you please open a window and let a draft in, it's getting too hot in here. Most often you will hear of a draft in the context of someone looking for it to cover it up or patch it and get rid of it. A draft is basically an unwanted invasion of air into a room in a home that should otherwise be of a nice temperature, making dream interpretation of this symbol even richer with metaphor.
If you have a dream about a draft then this means that you need to try the best that you can to make sure that everything in your life is air tight. You are doing a lot of work to make sure that you have done everything that you have needed to do in life. You can sometimes leave out some major gaps if your head isn't in the right place or you just overlooked something. Don't let this happen to you, just remember that you need to close off that draft before it ruins the integrity of the whole thing. This is what you need to know.
A draft can also mean that you have let some miscellaneous malignant force into your life recently and it is slowly chipping away at you. You likely will not notice all of the negative effects at first and it will take you some time to get used to the idea of something like this having such a major effect on your life, but it is something that you will no doubt have to grapple with one day and the fact that you are having this dream is an indication that they day will come to you sooner rather than later.
Basically you should begin to consider all of the things that have gone wrong in your life recently and start to wonder if it is possible for you to patch up some of the holes. The worst thing is, a draft may even seem pleasant at first but then one day turn to an annoyance when the weather outside changes. This is a bit of a complex metaphor but the idea is, you could have let something into your life recently which at first seemed like a blessing, but now circumstances have changed at what once seemed like a great influence has now become a terrible one. This kind of thing happens most often with relationships. You let someone into your life because you were hurting and they were there to comfort you in your time of need, but now you've had some time to come to grips with what you were dealing with before, now you need to take some time to combat all of the adversity you're feeling and the person that you let in earlier seems to be working against you. Perhaps they think you won't want them still once you feel better, but whatever the case is, though this is quite a specific example, something like this situation is happening in your life and it is why you are dreaming of a draft.