Both of her parents and her grandfather have dark eyebrows and both Anna and Elsa have dark eyebrows from an early age (even before Elsa's hair turns white as a result of her ice powers developing). This appears to be a genetic trait of their family.
Note that this is perfectly normal in our mundane world.
Genetically speaking, hair color is pretty complex. "The genes that
determine hair color are so-called 'incomplete dominant hereditary
traits.' This means that there isn't one single gene that's dominant
over the rest, but all genes influence each other," Petra Haak-Bloem,
specialist at the centre, tells me.
The same genes can express themselves differently for anyone. That
allows for lots of possibilities, one of which is that the color of
your head hair differs from the color of your armpit hair, pubes, or
beard.
"Generally speaking, people inherit hair color not only from their
parents, but also from their grandparents and earlier ancestors. So
it's entirely possible that one distant ancestor had a hair color that
suddenly appears again though a certain combination of genes—and that
can be quite unexpected for parents," Haak-Bloem continued.
Why Do So Many Men Have Red Beards But Not Red Hair?