Snowfeather Hatchling
Source: Drop. Snowfeather falcosaur hatchlings instinctively flee to nearby adults when threatened. The species is particularly fond of large prey. Flying type. Worked on the quests on different characters. You can get a new quest on one character and complete it on a different character.
The Snowfeather Hatchling is a falcosaur battle pet found in Highmountain during Legion, obtained by defeating the Snowfeather Matriarch during an active falcosaur World Quest and then feeding the orphaned hatchling 
Smoked Elderhorn.
Guide awaiting review
Wait for Falcosaur World Quest
The Snowfeather Matriarch only appears in Highmountain when the Snowfeather Swarm! World Quest is active. You can still capture the hatchling even if you have already completed the World Quest previously.
Obtain Smoked Elderhorn
Purchase one Smoked Elderhorn from Marius Felbane at 29.8, 40 in Highmountain before heading to the Matriarch. You only need one piece.
Defeat the Snowfeather Matriarch
Head to the Snowfeather Matriarch at 35.1, 21.9 in Highmountain and defeat her. She has a respawn timer of around 5 minutes if she needs to be re-killed.
Find the Orphaned Snowfeather
After the Matriarch is defeated, head to 32.5, 28.2 in Highmountain to find the orphaned Snowfeather hatchling. It will NOT appear as a green paw on your minimap, so navigate there manually. If the hatchling is not present, use your Flightmaster's Whistle to the nearest flight point, return, re-kill the Matriarch, then go back to 32.5, 28.2.
Feed and Capture the Hatchling
Interact with the orphaned Snowfeather and feed it the Smoked Elderhorn to tame it. Confirm that you have not reached your maximum pet cap before interacting, or you will be unable to add it to your collection.
Level Your Hatchling to Max
Level the Snowfeather Hatchling to its maximum level to begin the mount quest chain — 
Ultimate Battle-Training Stones can be used to speed this process up.
Visit Your Faction Inn
With the Snowfeather Hatchling summoned or in your battle team, visit an inn in your faction's capital city — Orgrimmar for Horde or Stormwind for Alliance — to pick up the next quest in the chain.
Beat 3 Wild Pets in Highmountain
With your Snowfeather Hatchling summoned or in your team, defeat 3 wild pets in Highmountain, which is the zone where you found your hatchling. The quest will select random pets from that zone.
Complete 5 Highmountain World Quests
Complete 5 World Quests in Highmountain with your Snowfeather Hatchling summoned or in your battle team throughout this entire quest chain.
Complete 3 Pet Battle World Quests
Complete 3 Pet Battle World Quests in any zone in the Broken Isles with your Snowfeather Hatchling summoned or in your team.
Complete 1 Rare Elite World Quest
Complete 1 Rare Elite World Quest (indicated by a blue quest icon with a dragon outline) in any zone. World Quests located inside dungeons do not count toward this requirement.
Tips
Quest progress for the Snowfeather Hatchling quest chain can be made on different characters — you can pick up a new quest step on one character and complete it on another, including characters that have previously completed a step.
See the video guide for a full walkthrough of the capture and quest chain process.
