Groundhog Day in the U.S. is based on Candlemas, one of the pagan celebrations that's still around in a bastardized sort of way. Candlemas was originally halfway between the Winter Solstice and the Spring Equinox and supposedly the weather on that day could predict the end of winter:
According to the old English saying:
If Candlemas be fair and bright,
Winter has another flight.
If Candlemas brings clouds and rain,
Winter will not come again.
From Scotland:
If Candlemas Day is bright and clear,
There'll be two winters in the year.
From Germany:
For as the sun shines on Candlemas Day,
So far will the snow swirl until May.
For as the snow blows on Candlemas Day,
So far will the sun shine before May.
And from America:
If the sun shines on Groundhog Day;
Half the fuel and half the hay.