Unfortunately, I understand this completely, because I also have a character I play off and on that's exactly this morbid. No one in this group should ever meet them. ...Also, I know an unfortunate amount about frozen corpses, and I don't want to explain why!!!

It'll be able to be cut into pieces, but as it begins to thaw, the corpse will start to deteriorate. If they want to keep their pieces intact, they'll have to find some way to keep it cool.

Which comes to the other definitely unrelated question: they're likely to be suspicious if they smell or see anything different. Do it well enough and hide them well enough, and you might just get away with graverobbing.