Story Content before HoT
While I do recommend doing the guild wars 2 personal story when you have the time, I don’t think it will be necessary to complete it prior to HoT. Though you might not know some of the returning characters. However I do think it would be a good idea to to catch up on the content of season 1 and 2 of the living story, because those tell the story leading up to the content in HoT.
Season 1 is not available anymore in the game, but there is a small summary on the story if you talk to Magister Ela Makkay (http://wiki.guildwars2.com/wiki/Magister_Ela_Makkay). Season 2 can still be done, though you might have to buy the missions from the gemstore.
Thank you, Moon. That’s useful information.