All of the following items need confirmation, but appear to be valid as of the December 2012 patch. More samples are needed.
The Holiday Hearth, Pack Scold, Pack Abominable Snowman, Doll House and Holiday Feast may be the only rewards available in your Frozen Present if you received it from the Mayor when showing him a Hot Coal.
The Frozen Presents looted from the Abominable Snowman commonly yield most of the rest of the rewards from the list of possible items.
These observations are from the current (December 2012) patch, and are based on approximately 264 total Frozen Presents from a combination of both sources: 168 of 168 Frozen Presents received from the Mayor yielded either a Holiday Hearth, Pack Scold, Pack Abominable Snowman, Doll House or Holiday Feast only. The remaining 96 Frozen Presents were looted from the Abominable Snowman, and thus far have contained a fairly even distribution of all other items EXCEPT for the Holiday Hearth, Pack Scold, Abominable Snowman, Doll House, Holiday Feast, Big Wreath (unconfirmed to drop from Frozen Presents), or Orb of Eternal Frost (known to be rare).
It appears thus far that only the Frozen Presents looted from the Abominable Snowman have any chance of containing the newer rewards introduced since the quest was originally launched.
--Specterk 21:58, 6 January 2013 (EST)