Eventually you will get a quest titled “Track An Escaped Demon” in Shin Megami Tensei IV: Apocalypse that lets you hunt down Black Frost. The demon is located at Yaesu Passage and this guide shows you how to find him and defeat him.
How to get to Yaesu Passage
Use a terminal to travel to Shinjuku and follow the green arrow in the screenshot below :
When you get to Yaesu Passage, go straight and turn left. You will eventually reach a room.
Black Frost’s weakness and how to defeat him
Black Frost blocks fire and ice type skills. In addition, he also has resistance to physical attacks, however, he is weak to light skills (although they may not insta-kill him).
When selecting demons for your party, make sure they are not weak to dark and ice skills. You may also want to stay away from skills with low accuracy since Black Frost has a dark skill which can eliminate your entire team with a skirmish.
If you can get access to clothes that protects you from dark skills, make that a priority. Otherwise, keep a demon that resists dark skills and have a skill to bring back a teammate to life (such as Recharm) in your party during the battle.
Other than those points, use the information above effectively and you’ll eventually bring the snowman down.