Why does the princess get cold? (Spoilers)

[JRPG-Guy]

After the end of each path the princess starts to get cold then she's taken away my multiple arms to be assimilated to her original self? Is there a reason for the chill. And What's with the multiple arms?

[KaeWhy]

The Mound says she takes each Princess' consciousness to assimilate them into herself and leaves an empty vessel behind... so they're effectively "dying" and becoming part of her.

[Cel]

The void is cold.

[yamidamian]

The princess is Death and Entropy, among other things. When she feels cold, that's a sign her greater self is about to reach out and take her. The Hand of Death being a cold one is a common symbolism.
As for the arms-those would be said Hands of Death, reaching out to take the vessels into herself, to become more complete.

[Rank Zero]

The question already has a solid answer, but it's worth adding that the Spectre is cold-themed and killing the Princess in chapter 1 awakens the Voice of The Cold. So there's some in-context associations between coldness and death.

[CrabNicholson]

They're cold because they're dying. The multiple arms is symbolic for how the princess is more than just a single form.