You should not run to get fit, you have to be fit to run.
Ask yourself, is your body "fit" for the daily recreational tasks you ask it to perform? January-March is a great month to get yourself fit to tolerate the mileage and racing you may have planned for the warmer months. Here are two scenarios that I implore you to avoid:
1. Neglect to perform additional strengthening and cross training during the off-season and find yourself disappointed in your performance at your first race in May. You could tell that you lacked the power to get up those hills as quickly as your fellow racer and you decide you had better start doing some extra strengthening in order to "get your butt in gear" for your next race in June. So, you hit the high intensity strength workouts at your local fitness center. Your body's tissues can't take the additional loads from strength training in addition to continued increase your weekly mileage, and you end up with muscle strain or tendonitis, forcing you to take weeks off of running.
2. Decide that you want to "get fit" as a new years resolution and start running off-the-couch as your method to do so. After 3 weeks of running for 30 minutes every day on your lunch break, your knee starts to hurt, and you give up on running. I'm not saying you shouldn't start running, just make sure your progression is gradual (10-20% increase in weakly mileage) and assure you are performing some routine strengthening routine in addition to a gradual increase in your running mileage. Strengthening should focus on core and hip stability exercises as well as dynamic single leg balance and squatting.