Christmas and New Year's
The play is set during the holidays. Yes, it's Christmas time for the Helmers and New Year's is swiftly approaching. Chances are that this isn't random. Christmas and New Year's are both associated with rebirth and renewal. Several of the characters go through a kind of rebirth over the course of the play.
Both Nora and Torvald have a spiritual awakening, which could be seen as a rebirth. Nora's trials and tribulations wake her up to the pitiful state of her marriage. When the "wonderful thing" fails to happen, she realizes she'll never be a fully realized person until she severs herself from her husband. When she slams the door behind her, she is in a way reborn. Nora is not alone in her spiritual awakening, however. Torvald's last line, "The most wonderful thing of all?" (3.381), seems to indicate that Nora's words haven't fallen on deaf ears. Torvald, like his wife, has realized the complete inadequacy of his existence. By the end of the play, both Helmers have been reborn.
Krogstad and Christine are reborn as well. When these "two shipwrecked people […] join forces" (3.42), they each get a fresh start in life. Both of them view their renewed love affair as a chance for salvation. Krogstad hopes that it will help increase his standing with the community, and that Christine's influence will make him a better person. Christine is overjoyed that she will have someone to care for. She once again has purpose in her life. Yes, it seems that, in A Doll's House, 'tis the season for rebirth.
The Christmas tree itself can also be seen as symbolic. For one, its presence reminds us what season it is, and brings to mind all the points made in the above section. Beyond that, however, it can be seen as being directly symbolic of Nora. How, you ask?
First of all, the tree seems to mimic Nora's psychological state. At the beginning of Act Two, stage directions tell us, "The Christmas Tree is […] stripped of its ornaments and with burnt-down candle-ends on its disheveled branches" (2.1). But what does that have to do with Nora? Stage directions go on to say that, "[Nora] is alone in the room, walking about uneasily" (2.1). Basically, Nora is a mess and so is the tree. She's gotten the bad news from Krogstad, and as a result her mind is just as disheveled as the tree.
You could also interpret the tree's state as symbolic of Nora's disintegrating web of lies. The pretty decorations which Nora used to cover up her deceit are falling away. Soon the bare ugly truth will emerge.
Lastly, Nora's function in the household is pretty much the same as the tree. She's merely decorative, ornamental if you will. She dresses up the tree just as Torvald dresses up her for the Stenborgs' party. It's interesting that she tells the maid not to let the children see the tree until it's decorated. This is reminiscent of when she tells Torvald that she can't be seen in her costume until the party. It seems that Ibsen built in many parallels between Nora and her tree.