Assuming that
Disneyland is once again going to celebrate Three Kings Day -- which has been capping off the holiday season at DLR for the last few years -- then the in-park decorations and holiday events should stay up/open through
at least Wednesday, January 6th. Disney could be ambitious, however, and keep the holiday season in full effect through Sunday, January 10th.
If they don't do a Three Kings Day celebration in 2016, then the holidays could end as early as Sunday, January 3rd (with the 3rd being the last day).
As figment_jii pointed out, usually Haunted Mansion Holiday closes first to have its holiday overlay removed, then when it reopens IASW Holiday closes to have its overlay removed. IASWH usually stays open through the MLK holiday.
This past holiday season, because Frozen Fun was introduced in the second half of December 2014 as a preview, and then it officially opened on January 7th, my guess was that Haunted Mansion Holiday was kept open a bit longer to entertain all of the people descending on DLR for Frozen Fun.
This time around, no one knows if all elements of Frozen Fun will be returning (meaning Olaf's Snow Fest and Freeze the Night) -- and, if so, will they return at the start of the holiday season, or at the end of the holiday season, or somewhere in the middle?
This past season also included an extended schedule for Olaf's Frozen Ice Rink and the Winter Village in Downtown Disney. Normally, those would have been closed down as soon as the holidays ended, but they stayed in place until February 22nd, in conjunction with the Frozen Fun going on in the parks.
The 3 Disney hotels kept their decorations up a bit longer this past holiday season as well. Ordinarily, the hotels' trees and décor have come down either immediately after New Year's Day -- or, in some years, even after Christmas and before New Year's Eve. This past January, the Grand Californian Hotel's gingerbread house (in the lobby) stayed up through at least January 6th, and I think the tree stayed up as well.
If you go to DLR during the first week of January -- meaning somewhere between Monday, January 4th and Sunday, January 10th, I think you have a very good chance of seeing most, if not all, of the holiday offerings -- especially in the first half of that week. Santa Claus might be gone from his posts at that point, but I am guessing that won't matter since you're going in January!
If you go after January 10th, you may only end up with IASW Holiday and the decorations in the immediate IASWH area.
But this year is a big question mark in terms of when things are going to start and end, and in terms of which decorations will be up and which seasonal events will even be happening, so it is all a mystery right now!