As the supercooled drop falls out of the warm layer, it contains all water (and possibly an ice nuclei). Assuming it is all liquid, the drop will liekly to freeze at -10C or below as the ice nucleii is activated. However, it will freeze from the outside-in and likely splinter into ice fragments. Also, it could simply freeze around the nucleii or if another piece of ice were to encounter the drop, it would form more of an ice cude or graupel. QUICK FREEZE!
Snow would form on an ice nucleii that were suspended in the near-surface layer if the layer were saturated and below -10C. Simply growth of water vapor onto the ice nucleii to create snow flakes...this is separate from the vertically falling liquid in the above sleet scenario.
So, you actually have dual precipitation processes going in this tough scenario and likely a mix will result.