Here's the easy way to think about it: figure out how much
enthalpy you have to put in to warm the supercooled water,
moving along the red curve from (say) -40C to 0C. Then
imagine taking exactly that much enthalpy out at 0C, as
the ice forms, moving downward on the diagram along the
vertical line-segment at 0C.
Disclaimer: I have no data as to the enthalpy of supercooled
water. I freehanded the red curve by extrapolating from the
non-supercooled liquid. I reckon this is plenty accurate
enough for present purposes. The point is that none of the
supercooled water's behavior is much different from the
ordinary liquid's behavior.
(In contrast, the rest of the curve, i.e. the blue and black
parts, are real well-attested quantitative data.)