Placing Ice Counters on monsters the opponent controls and destroying a card the opponent controls are not targeting effects. Each card that needs to be chosen is chosen at the resolution.
Destroying a card the opponent controls is part of the effect that places Ice Counters on monsters the opponent controls. It doesn't start a new chain.
The effect that destroys cards the opponent controls is applied if a single copy of this card activates its effect and in that single activation it places 3 or more Ice Counters among monsters the opponent controls.
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Konami OCG Card Database: Snowman Creator
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