When I am training for a race, be it a short 5k or a marathon, and i want to set a specific time, i will often mix in running on a treadmill to set a pace. When you run you naturally start to run slower when you get tired, but it doesn't feel like you are running slower, because you are progressively getting more tired. The treadmill neutralizes that, because it forces you to keep running at the same pace. That is why I like using a treadmill, occasionally. But you should still run outside to get used to the idea of running in the cold.
Based upon your comments, I suggest you run every other day, and alternate running outside and inside on a treadmill. When you run outside, run 2 to 3 miles, at a "comfortably fast" pace. You don't have a lot of time before you take the test, so you need to make the most of your training. Running 2 to 3 miles will give you a lot of stamina, and make running 1.5 miles seem easy. The other days you will run inside on the treadmill at just faster than your goal pace of 8:30 minutes per mile (you need to run 1.5 miles at just over an 8:30 minute per mile pace). Most treadmills set their speed by miles per hour -- an 8:30 minute mile is 7.0 miles per hour, so I suggest running at 7.1 miles per hour to give yourself a small cushion. Set the treadmill at 7.1 miles per hour and try to run for the complete 1.5 miles. If you can't do it at the start, fine, just try your hardest, and work up to 1.5 miles. After you can can run 1.5 miles at 7.1 miles per hour, start to add some incline to to the treadmill for half of the run (a very small amount of incline makes it significantly harder, so don't go crazy cranking up the incline). After you have done that a few times, see if you can run further than 1.5 miles at 7.1 miles per hour, with incline.
Based upon your comments, you should be able to do this easy. The other thing you need to remember is that you will have a lot of adrenalin coursing through your body on the day of the test, which will make it easier to run faster. The only trick to that is that you need to be careful not to run too fast at the start and then be too tired to keep running at the end. This is another reason why using the treadmill is a good idea, because it will give you a feel for what is the right pace. If you run enough, you "know" your pace without needing a watch.
Good luck. I'll be happy to answer any other specific questions you might have.