Snowin' Snowmen

The game is simple - you have just 2 rules:

1. CATCH AND STACK SNOW

Snowballs a meter in diameter are falling. Everywhere. Some people get worried, but they don't see the big picture. They complain about being snowed in or snowed out, apocalypse or whatever, but they just can't see what kind of opportunity we have here. For millennia men have competed over who can build the tallest tower. But we have entered into a new age. We must build the TALLEST SNOWMAN EVER!!

2. AVOID SNOW HEADS

Scientists and philosophers alike are baffled as to how (and why) giant fully assembled snowman heads fall from the sky.
"Where did they come from?"
"Who made them?"
"Does everyone get free carrots and top hats?"

All Valid questions... for the naive and shortsighted, not you nor I. We are doers - innovators and we know those snow heads are nothing but obstacles. We are to avoid them at all cost!

"Really?", you'll might ask, "I thought as we were building the world's tallest snowman, giant fully assembled snowman heads would be strangely convenient." Well you seem to have forgotten that a snowman head goes at the TOP of the snowman. As soon as we get one of those heads we can build it no higher! In no time you've gone from limitless to limited. From possible to impossible. From approaching the TALLEST SNOWMAN ACHIEVABLE to a fairly tall snowman. Ahem, lost myself there - in short avoid the heads.

But I leave this to you - just you and unlimited snow. What will you do with it?

(hint) build a really tall snowman!