Ice powers = Drug addiction?
Here's my take on the somewhat "metaphor" that the ice powers could be representing... it only occurred to me recently after hearing some past stories of people who lost their lives to drug addiction, and how their families dealt with it.
Elsa's ice powers are something that she and her sister, Anna, seem to enjoy as young kids. It was always something they had to keep quiet, so when they're playing around with her ice powers, it's then they feel the most happy. As you would, if you took some form of hallucinogen. However, Elsa zapping Anna's head and her falling unconscious is like Anna having a bad reaction to the drug, so the trolls, by erasing her memory, is like them helping her stay off the drugs.
Meanwhile, during their time apart, Elsa's parents try to make sure she dials down on the drugs, but she cannot help her addiction, and no matter what, her will power just isn't strong enough. The further away Anna stays from Elsa and her addiction, the less she's going to feel influenced.
However, after Elsa's secret addiction is exposed, she then decides to embrace it. Some drugs are known to take away any negative feelings, and her building the castle is the high point of the drugs making her feel good and not worrying about anything anymore. Plus, Elsa begins to feel distant to her own sister, as drugs would make you feel distant to even some of your closest family members, sometimes, you forget your own family's love in favor of the hallucinogen. Not to mention that your addiction can affect other people's lives the same way Elsa's ice powers affect the people in the kingdom.
As we all know, drug addiction can get to a point where the addict's health is at risk, and the only way out seems to be to put them out of their misery. Many see this as the way out of the cursed winter, and nobody else will have to suffer. However, Anna believes that she can help Elsa by calming down her powers, in other words, calming down her doses, and everything remains healthy and back to normal.
Don't kill, just take it easy...