Currently the blue partyhat is the most expensive partyhat and is in front of the white partyhat.
They can only be obtained by trading with other players due or by purchasing from the Grand Exchange due to the fact they are discontinued. They are generally used to show how wealthy a player is and has no actual bonuses.
During the Christmas 2013 event, a bonfire in the event area gave a health boost after 5 logs have been added to it. The health boost from this bonfire lasted for 10% longer than normal bonfires and those who got the health boost in this way received a 1% Firemaking XP boost when wearing the blue partyhat (and 1% more for each additional Christmas item) they were wearing while using the bonfire. The bonus XP capped at 5%.
During the 2013 Christmas period (00:00 GMT December 20th 2013 until 23:59 GMT January 3rd 2014) this item counted towards the Blessing of Winter buff – wearing Christmas gear would increase the drop chance of festive crackers by 20% of the original chance and also provide you with hybrid stats appropriate for your level.