It's my impression that the parks still have near-New-Year's-level crowds until school starts--so the exact date varies year to year. After that, crowd levels definitely diminish with the exception of MLK weekend, which is always busy.
Also be aware that it can be difficult to secure a room during marathon weekend (usually sometime around the 10th or 11th of January), but this doesn't really affect park crowd levels, just booking a room on site.
The rest of January is blissfully empty.