There could be a relationship between Sun sign and behavior, if it is presumed that the amount of sun a newborn gets has any effect - e.g., a Scorpio would not get a lot of Sun (in the higher latitudes of the Northern Hemisphere) until he reaches about 6 months in the following Spring. Also if there is some correlation between parents' sexual activity and the time of the year, and the behavioral outcome of the child.
Oh, there's definitely some correlation between sun-sign and general personality traits - I see it all the time.
It's absolutely
nothing to do with star positions though, that side of it is just a
bunch of woo-woo...
Your idea about the amount of sunlight a baby gets (and weather in general) may well be a factor - And personally I think it may well be a whole lot of other environmental things also.
During those first few months, a baby is like a sponge, totally helpless and soaking up everything that's going on around them.
Not just the weather, but during winter months they'll be kept indoors more, spending more hours per day in close proximity with family members - The run up to Christmas there'll be a general optimism among most people - around Christmas, a lot of social get-togethers indoors - the couple of months after the turn of the year a lot of people are on a bit of a downer.... and other things throughout the year.
It's perfectly feasible that a new-born baby will soak up a very different atmosphere depending on what month they're born - and may well have an influence on how their personality turns out.