I took a meteorology course at university years ago.
On Feb 2, the lecturer (who was a strange old hippy) gave a lecture on weather folklore and mythology and if any of it had a basis in reality.
His take on Groundhog Day, was that it was actually based on real observations…and he had stats and science to back it up.
He said if you take the number of hours of sunshine in the first week of February…and then graph it next to the average daily temperatures for the first week of March there was a strong correlation. A lot of sunlight in early February generally correlated with colder temperatures in March….and vice versa.
His explanation was that the jet stream moves and stays further south in the winter, then starts to move north as winter ends. While the jet stream is further south, it means high pressure, clear weather for middle lattituds, but as the jet stream moves north it brings unsettled, cloudy weather.
So a lot of sunny weather in Feb means that the jet stream is still in winter mode, but a lot of cloudy weather in Feb means that the jet stream is on the move into spring.

Now, one hour with a groundhog is probably meaningless, but an entire weeks worth of observations can show something…and that people started to notice that a lot of sunny days in early February often signalled continueing cold weather….

So…science.