I am very much almost certain that Frost is a recessive pied, but I am not 100% sure because her wings and stripe color throw me off a bit.
Loki, I just downright have no clue. I've not seen a picture of any budgie that looks like him that states what kind of color mutation it is.
Frost's stripes and wing spots are not entirely black, they are more of a slightly darkened grey. The blue on her rump and belly are pale and slightly dull.
Loki, with the little markings he does have, are also not black, but are almost transparent to his yellow base feathers. If anything, they could be a light grey color. His belly has hints of green, but not much, his rump holds most of the green, which is very pale.
As a note, the camera darkened the colors on Loki and Frost much more than it really is. In the pictures their markings are not black, in real life they are very pale, and grey.