And now, an explanation of how Princess Anna didn’t die of hypothermia while wandering in the woods in winter soaking wet.
So to start a little science: human genes are carried on two sets of chromosomes. This means that genes come in pairs like socks. We get one sock from each parent. Of course they aren’t called socks; we call them alleles. Alleles can come in matching pairs or mismatched pairs. The mismatch can cause several things to happen. Sometimes you get recessive/dominance, wherein one allele shows the trait and the other allele is hidden. The gene for dimples is dominant. If your alleles are mismatched and you have one that says ‘have dimples’ and the other that says ‘don’t have dimples’ dominance wins and you have dimples.
Other alleles function in combination, each contributing to the trait. A pretty common example in textbooks is the flowers called Four-O’Clocks, for which a red allele and a white allele make a pink flower. This mixing is called codominance.
Yet another possible allelic interaction is incomplete dominance. In incomplete dominance your allelic choices are a trait or a null allele that doesn’t do anything. It’s almost like having one sock not be a sock at all. The sickle cell gene works this way. Anyone with two null alleles has normal red blood cells. Those having two sickle cell alleles have lots of sickled cells causing sickle cell disease. People with mismatched alleles though? They wind up being mostly ok. As it turns out, having only one allele for sickle red cells means you have a little bit of sickled red cells that can affect you sometimes, but not nearly to the severity that having two alleles will. Incomplete dominance means one allele gives you a little and two alleles give you alot.
So that said, I believe the trait for magical abilities pertaining to ice and snow are traits that manifest as incompletely dominant. Elsa and Anna have gotten their genes in allelic pairs from their parents. Queen-Mom and King-Dad must each be mixed in terms of alleles. They each have one non-magical allele and one ice allele. They do not manifest magical abilities because that takes two alleles. They have each handed down a single magical allele to Elsa, so that she got two. Anna on the other hand, received one magical allele and one non-magical. Elsa, having two ice alleles instead of just one, can harness enough ice power to actually affect her world by creating ice and snow and manipulating them. Anna has far less magical ice power, and it manifests as merely allowing her to withstand the cold without suffering significant harm. If put to the test, both parents should also have been rather more impervious to cold than humans with no magical alleles at all.
So there you go. The cold never bothered Anna anyway.