According to Jennifer Lee, even though the reason for Elsa's ice magic is never explained except for a mention that she was simply born with it, it has been hinted that the source of her magic may have been caused by a 1000-year alignment between Saturn and other distant planets like Uranus, Neptune, dwarf planets like Pluto, etc.; much like how Rapunzel got her blonde hair from the Sun's light.

For a young girl I used to babysit until strep throat took her. (She loved Frozen a lot)

~Cinderella