I am a freshman in college and a fourth class Midshipman. I am not receiving scholarship benefits even though I got the scholarship.
I started my application the August before the start of my senior year, put it in in December and had my interview in January. I got the scholarship but I didn't get my first choice of school because I applied so late. They gave me my second choice, but I didn't get in there and the third school already had a waitlist for transfers of scholarship as did the first. I eventually decided just to go to my first choice school but despite the fact that my family has to pay ridiculous amounts of money that it likely wouldn't if I had just applied earlier.
To sum it up, the earlier you finish your scholarship package and submit it, the more likely you are to be able to go to the school of your choice on scholarship. APPLY AS EARLY AS YOU CAN. (Unless you need to boost your grades, take the SAT again or otherwise improve something important).
Try to finish the application during the summer before senior year at the latest because you will obviously have to start applying to colleges and that will take much time and energy.