I think you are
February
I'm the shortest of all my brothers and sisters
February is the shortest month of the year.
I've never won first
It's also the second month.
I'm known to love the water
In astrology, the star signs Aquarius and Pisces overlap in February - both water signs.
And I leap with a burst
Every four years an extra day gets added for a leap year.
I also like it colder
February is usually counted as being at the end of Winter/beginning of Spring so is a bit colder (in the Northern hemisphere at least).
Title
February was one of the last months to be added to the Roman calendar