I do the exact same thing as this.

My overnight water in wintertime typically sits in a nalgene
buried upside down in snow, and in an aluminum GSI double boiler set with a thick blue foam cozy built around the pot - basically
the potset is enclosed in blue foam.

The top of the pot may freeze in really cold weather, but normally fine.

In the morning I then have water to heat up - and use to start
more snow melting to have water for the rest of the day.