A forecast is a prediction. It is primarily used when talking about the weather, but can be used in other matters, too. A deadline is a due date -- the final date of acceptance. You would not use the word "forecast" when talking about a deadline. You also do not need to use "to." The sentence you provided should be written like this: "The deadline of the project is December." You could also write, "The project's deadline is in December."

A forecast is a prediction of when something might happen. Emphasis on might. A deadline is the definite time that something when will happen. Emphasis on will.