宀 pictures a peaked roof and frames the scene: someone sheltering indoors. As the indexing radical it places 寒 among shelter-related chars like 家, 室, 安, 寝, even though the cold-feeling here pushes the meaning past simple housing.
semantic
寒hán
graphic residue: bundles of straw with a person inside
The middle is a stylised remnant of the original graph - bundles of straw piled around a huddling person. Reform fused those grass-and-body strokes into this 7-stroke lattice that no longer reads as any standalone char, so it survives only as part of 寒 itself.
冫 is the ice radical - two frozen droplets. Sitting at the floor of the house under the straw-and-body residue above, it pushes the whole composition from sheltered to bone-cold: ice underfoot turns the indoor scene into the feeling of winter chill.
