The shift of the blanket and the insulation charm keeps the small source of Sam's body heat from escaping. Though it is not enough to warm her up enough to remove her from the cage. Her skin was still a blue hue, her legs too stiff for her to move. The moment you grab and her try hauling her out of the cage is when she finally speaks, "D - D - D - Dor - Dora." It is her way of saying that she cannot move just yet. It hurt.

Patience, young Gryffindor. She needs time to thaw out.

Only the Finite spell you casted doesn't help her warm up any faster. In fact, the moment it is casted, the charms you had casted on her in an effort to keep her warm go out and she shivers. There were no hidden charms or spells keeping her from staying so cold. It was the elements themselves keeping her so frigid. The insulation charm that followed did nothing, for there was no warm air to insulate. Perhaps you should have casted that warming charm, which was working, first.

At this rate, the best thing for Sam was to find some sort of shelter from the freezing elements of the tundra. The wind coming from the north is still blowing south if you wish to head in that direction. Just keep in mind that moving quickly was going to be a challenge with Sam still being quite frozen.