Here is a great summary of how the quest works. You are correct in thinking it is due to the Ashe and Sejauni, and not due to it being on the Howling Abyss.
From the League of Legends Wikia:
The event begins a seemingly random length of time after the following
conditions have been met, and can only occur once per game:
- There must only be one Freljordian leader per team. Having 2 or more
will not cause the event to work.
- The champions involved must have a sum of 20 kills + assists. (ex:
Sejuani has 3 kills and 17 assists. Adding them equals an exact 20.)
- One Freljordian leader must be level 16 for the event to start.
After a few seconds of meeting the said requirements, the event will
occur. The champions involved will say a unique quote at the start and
end of the event.
The victor will be given a permanent buff called, Queen of the
Freljord, and an ice crown floating above her head.
To complete the event, one of the leaders must kill or assist in killing the opposing leader. Then you hear a unique taunt based on the participants (These can be viewed on the League of Legends Wikia)