You should be able to find the Crown Spire in a Snowy Plains biome

Before entering the spire, take a look to the right of the building. The back right ice spire has a hidden barrel. Walk up to it, find the warped fungus, and break this ice block that's facing it. You should find the barrel with the Calyrex Crown in it.

Continuing around the spire, you should see a carrot patch. One of them will be blue, and is actually an Iceroot Carrot. Break this and walk over to the composters and spruce trapdoors. Throw the carrot on top of the composters. The ice peak behind the composters will open up and Glastrier will spawn there.

There are many barrels, books, and pokedolls for you to loot, read, and take here. Nothing too much of note except for a lot of tera shards. Climb the ladders all way to the top and you should see a Calyrex Statue. Place the Calyrex Crown on the Calyrex Statue, and Calyrex will spawn.

Once you have both Calyrex and Glastrier, all you will need to make Calyrex Ice Rider is a Reins of Unity. Throw out Glastrier and right click on him with the Reins of Unity. You should see that they are now "charged" (see image below). Then, right click on Calyrex with the charged Reins of Unity and you will have a Calyrex Ice Rider.