Interest you pay on a home mortgage is tax deductible for the year in which it was paid. By making January's payment in late December, you not only get a little ahead, but you get to deduct the mortgage interest you pay in this tax year, not next year. Say sending an early payment results in an additional $100 or $200 on your income tax refund; in effect you get that money a year earlier than you would have by waiting a couple weeks to send in your mortgage payment.
Just make sure you send the payment in with the proper payment slip or otherwise make sure the lender knows you're making a payment ahead of time instead of sending in extra money that should go to paying down your principal balance. Some lenders assume additional or early payments should go to paying down principal, not to making an early payment.