One of the main quests in Pokémon Sword and Shield second DLC will have you investigating the mysterious King of Bountiful Harvests. In Crown Tundra, there is indeed a Legendary Pokémon that was once capable of growing crops at high speed to help the inhabitants. By the name of Calyrex, you will meet him fairly early in your quest and he will ask you to help him regain his powers (and therefore his faithful horse).
When you arrive at Freezington, Peony will introduce you to the village and your home. He will also tell you about the legends of the Crown Tundra and then give you his personal notes on the subject.
In the house, take the famous "pillow" of Peony which is on the table. This is actually the missing crown on the wooden statue outside. Return it to the correct location to summon the Legendary Calyrex.
Calyrex will then ask you to go and investigate it with the villagers. Talk to everyone until a message appears on your screen telling you to return to the Pokémon.
Once these conditions are met, you will be able to freely explore the region.
Talk to the village chief
In order to gather more information on Calyrex, you will need to speak to the Village Chief. He will then tell you that the Legendary had a Steed sometimes described as White, formerly described as Black. We then understand that there are two capturable forms of Calyrex (it will be up to you to choose which one you want).
We also learn that to attract this Horse, you must plant an Iceroot carrot (for the white form) or a Shaderoot carrot (for the black form).
Calyrex will show you the lands where it's possible to plant carrots.
Speak with the old man tending to the crops in the center of Freezington to obtain Carrot Seeds (it costs 8 Dynite Ore.)
Where to plant Iceroot carrot to get Glastrier
If you want to get the white form of Calyrex's Horse, you must plant the Carrot seeds in the land surrounded by snow. The field is located at the entrance to the Snowside Slope, behind a small pond.
Then collect the Iceroot carrot. Glastrier will make an appearance and gallop to Freezington. You can then fight it on the spot but not capture it. To do this, you will first need to craft the Reins of Unity.
Where to plant Shaderoot carrot to get Spectrier
If you want to get the black form of Calyrex's Horse, you need to plant Carrot seeds in the land surrounded by a burial ground. The field is located in the Old Cemetery (east of Giant's Bed).
Then collect the Shaderoot Carrot. Spectrier will make an appearance and gallop to Freezington. You can then fight it on the spot but not capture it. To do this, you will first need to craft the Reins of Unity.
How to get the Reins of Unity
Whether you chose the Iceroot or Shaderoot Carrot, you will need to craft the Reins of Unity in order to catch Calyrex. After your fight against Glastrier or Spectrier, the latter will drop a tuft of Horsehair (dark or icy) to the ground. Pick them up and return to Calyrex. The latter will then give you the second necessary element: a Radiant Petal.
Go see the Village Chief to make the Reins of Unity.
How to catch Ice Rider Calyrex or Shadow Rider Calyrex
Once the Reins of Unity and the Carrot are in your possession, you must go to the top of the mountain, to the Crown Shrine.
Once at the summit, place the Carrot (Iceroot or Shaderoot) in the container on the left.
At level 80, your fight against Spectrier or Glastrier can then begin, and this time: you can capture him!
Requires Iceroot Carrot and Reins of Unity
Psychic and Ice Types
Requires Shaderoot Carrot and Reins of Unity
Psychic and Ghost types
Swords of Justice are present in Pokémon Sword and Shield DLC, but you have to search for footprints in the Crown Tundra to find them.