This question presupposes that celebrating secular New Year's Eve in the first place is OK. I looked here: " Is it ok to celebrate New Years Eve? " and the answers seemed not fully resolved, but my reading of them is that it is not forbidden.
Having said that, for many people New Year is associated with the New Year tree (which is a spruce/pine tree). Is that part of New Year celebrations OK for a Jew?
One one hand, the origin of New Year tree is almost certainly/clearly that of a Christmas tree, which to me would definitely seem problematic at best.
On the other hand, for many people (for examples Jews raised in USSR, where Xmas wasn't celebrated for close to 100 years), the tree is 100% firmly and surely only associated with secular New Year, without any connotation of Xmas.
This is almost certainly Ḥukath HaGoyim. Please see the answers there for more information on what makes something fall into that category, but in general, anything done with either no obvious origin (and no logical basis) or an idolatrous basis is prohibited. Debate about the permissibility of marking the first of January as the start of a new calendar cycle aside, standing up and decorating a pine tree for that purpose would seem (to me) to be squarely in that zone.
No source about this particular practice; sources for the general terms of the prohibition available at the linked question and its answers.