Why does snow in a freezer turn to ice and become hard?

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When the last snow fell I picked some up and put it in the freezer,
sealed in a plastic bag to keep moisture out. I hoped I'd be able to
get it out in the summer and throw a snowball at someone on the
hottest day of the year.

It didn't work. After a few months in the freezer the snow turned to
ice, and throwing a lump of ice at somebody isn't funny.

Basically I'd like to be able to preserve a handful of snow from
January until June, and be able to get it out again in the same fluffy
condition it was in when I picked it up. How can I achieve this?

What physical processes are responsible for turning the snow to ice?
I thought I'd protected it against moisture from the air, by sealing
the snow in a plastic "zip lock" bag. Maybe my freezer isn't cold
enough? How cold does it need to be?
 
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The problem most likely arises from your freezer going through defrosting cycles. It gets just warm enough for the snow to melt slightly but not enough for things kept in the freezer to thaw. Then when the freezer goes back into normal mode, the slightly wet snow refreezes into a solid mass.
 
There's a potential problem even if the freezer doesn't ever get above 0°C. Equilibrium between the frozen snow and the water vapor in the bag means that ice will continually sublimate and condense while the snowball sits in the freezer. And there's no guarantee that the new ice crystals will form as light, fluffy snowflakes. In fact, it seems more likely that they'll deposit layers of solid ice.
 
Put it in a blender when you want to toss it at someone.