
Yes but they were stopped and it could have either reshutoka or aurora could've have sent someone too. Because the thing is If she truly didn't care what happens to karina she would've had NO reason to stop the prince from sending an army to get her.
Someone else said that her sister is evil and that the avalanche happened after she brought all those things to supposedly "Lure in Karina into the castle". Which again makes NO sense because it would be a huge waste of time and resources just to have the castle destroyed. However notice how the avalanche only occurs after Karina says she no longer cares what happens to the castle and that she no longer sees it as her home? In the storybook karina was reading they mentioned that the princess was "Blessed by the spirits of nature" and if you remember even the maid mentioned that after karina left strong tremors could be felt all over the area. The blizzard, the tremors and teh avalanche are all 100% connected to karina.
My years of reading manga leads me to the conclusion that this is a common case of misunderstanding troupe between the FL and her little sister. The only cure for this whole thing is the horrific and merciless downfall of that asshole prince and only him.