In Naruto, every shinobi has an affinity to their Chakra. This affinity can rest in one of the five basic elements: Fire, Wind, Lightning, Earth and Water. In order to discover one's affinity, it is used a piece of paper taken from a special tree that feeds with Chakra. By imprinting his or her Chakra in a piece of paper made of such tree, the person can discover what his or her affinity lies on depending on how the paper reacts:

Fire - it ignites and turns to ashes
Wind - it splits in two
Lightning - it wrinkles
Earth - it turns to dirt and crumbles
Water - it becomes wet/damp

After analyzing some characters and their elemental affinities, I've come to stablish a pattern linking each nature with a season (taking the northern hemisphere only). As you may know, each season spams through roughly three months and half. Spring begins in the end of March and ends in the middle of June. Summer begins in the end of June and ends in the middle of September. Fall begins in the end of September and ends in the middle of December. Winter begins in the end of December and ends in the middle of March

Now, this is what I understand:

Spring - Earth
Summer - Fire
Fall - Wind
Winter - Water

Now you must be wondering: What about Lightning? Well, since each third month (March, June, September, December) mark the transition between seasons, these months are associated with Lightning. So, this is what we have:

January - Water
February - Water
March - Lightning
April - Earth
May - Earth
June - Lightning
July - Fire
August - Fire
September - Lightning
October - Wind
November - Wind
December - Lightning

Of course this is not a rule, since there are exceptions, like Hiruzen Sarutobi, who has Earth as his primary nature. Bellow there is a list of characters whose nature - or primary nature in case of those having two natures - coincides with his or her birth season:

Spring-born characters who use Earth as nature/primary nature:

Deidara (May)

Summer-born characters who use Fire as nature/primary nature:

Sasuke Uchiha (July)
Fugaku Uchiha (August)

Midseason-born characters who use Lightning as nature/primary nature:

Kakashi Hatake (September)

Fall-born characters who use Wind as nature/primary nature:

Naruto Uzumaki (Ortober)
Asuma Sarutobi (October)
Orochimaru (October)

Winter-born characters who use Water as nature/primary nature:

Haku (January)
Suigetsu Hōzuki (February)
Tobirama Senju (February)
Yahiko (February)

As I said before, this is not to be seen as a rule. Actually, elemental affinity is something you have from birth, and just like color, you don't need to figure it at all, like finding an intricate astrological theory for that (seriously, sometimes you just have to listen to your heart, or else you will be driven mad trying to figure it). I for once, have a lifelong affinity to water (I FEEL connected to it, not only love it), even though, in the southern hemisphere standard, I was born on summer.