Tip: If you complete the 2015 Fae Yule Minion Adventure Chain, you will be able to complete a 1min Fae Yule adventure that has relatively short cooldown.
Players have been reporting getting the 1min Fae Yule chain every 5-20min (if you’re spamming the 1min adventures).
That said, Snedhepl estimated it probably has an ~4hr cooldown. Perhaps you are able to force it to reset if you use up all 1min adventures in the deck before their CD is over, probably causing the entire deck to reshuffle.
The 1min Fae Yule minion adventure is called “Grish has been banished from the land for now.” and is available until 7th Jan 2016.
Unlike most 1min adventures which don’t give any rewards (just minion exp), this particular 1min Fae Yule minion adventure has 6 reward tiers (separated into the 6 star rating). Be sure to send out the highest attribute value, closest-attributes-matching minion on the adventure!
(In this case, that’d be a minion like Dargal (7 Fire 18 Diplomacy). That’s an attribute value of 25 for the adventure. There’s also an internal dice roll. Those values put together will determine which star rating you get). [Minion Guide for Reward Tier explanation.]
This 1min adventure has similar loot table to the 10hr Fae Yule adventures. You might find it more cost-effective compared to doing the 10hrs, which cost 250 Aventurine to send out.
Unfortunately you won’t get anymore Troves; but the loot table includes Unique Snowflakes, past Fae Yule weapon skins, new and old Fae Yule dimension items, Fae Yule costumes and food. There’s also a chance at the limited currency for this event: Dark Icicles.
Unsure what Fae Yule or the 2015 Fae Yule Minion Adventure chain are? Check out these guides below:
RiftGrate 
I got the adventure way more often than every 4hours, more like all 30-40 adventures (every 5-10) minutes.
Yep, updated the article with the new info! 4hrs was based on Dev Snedhepl’s estimate, but it sounds like a forced adventure deck reset (when all cards are used up, without having enough time to go off CD) probably also resets the 1min Fae Yule card too.
This does not work for me. I spammed 100 minions back to back and it did not show a single time. I wonder if it had anything to do with the fact that I did the 2015 chain and then the 2014 chain. Maybe the 2014 canceled it because it was the last one I did? Or maybe its been hotfixed. In any event, not working now.
Perhaps the 2014 might have canceled it, but I can’t be sure. I’m still getting the 1min Fae Yule adventures, even today.
I haven’t done the 2014 chain and the quest isn’t showing up for me either, so I doubt it’s that – maybe it just bugged out/we have to wait until the server restart.
Sigh, it looks like my first post got ate. In any event, this does not work for me. Spammed 100 minions back to back and it did not appear a single time.