Winter Warlock/Father Winter/Snow Miser/Winterbolt?

I noticed several elements to back up the idea that the Winter Warlock was somehow connected with King Winterbolt. Almost all involve the magic skills shared by the two characters.
1) Both characters use magic snowballs to view the activites of others.

2) Both characters have magic feed corn that allows animals to fly (albeit it is never stated that King Winterbolt had this himself, but I can't see any way he could have stolen it from Santa).

3) Both characters live in a large ice castle. It is noteworthy that the Winter Warlock is said to live alone in his ice castle. This would be during the 1000-year sleep of Winterbolt. If they were associated, I would not be surprised at all if the Winter Warlock was simply living as a hermit in the castle, with his former master lying comatose.

4) The Winter Warlock lived in the territory that had been under Winterbolt's dominion (this is evidenced by the fact that, after Winterbolt's magically-induced sleep begins, the Kringles come to settle in his land. This is later distinguished from their trek to the North Pole with Santa. Since the Winter Warlock lived just up the mountain from the Kringles, he also lived in that same land.)

That's about that. A few final thoughts: I will concede that Father Winter (formerly the Winter Warlock) is actually a more likely candidate for father of Snow Miser and Heat Miser (and, I suppose, the new character of the North Wind).