Yes it's late. No beating around the bush here. It's it "too late," as you state? Well, it certainly diminishes your chances. As an applicant you want to give yourself all the opportunities you can, and submitting so late doesn't do anything to help you. Many schools will already be full by the time they receive your application and get around to reviewing it. Many schools may not be full, but won't be doing any more interviews.
What part of January are we talking about? Jan 1 is different from the last week in January.
Can you get accepted still? Sure. But you'll have a tougher go at it than if you had submitted in May or June or July.
The flip side to that is that if you have the funds and the mindset, then it can't hurt you to apply. You may get an acceptance, while the worst that will happen is that you'll not get any acceptances but still be more familiar with the application process than an average applicant.