ADDED: Emboldened by Mr. Lockwood's comment that this looks like "graupel," I add some information about the formation of graupel. From that impecable source, Wiki:
Graupel (also called soft hail or snow pellets) refers to precipitation that forms when supercooled droplets of water are collected and freeze on a falling snowflake, forming a 2–5 mm (0.079–0.197 in) ball of rime. Strictly speaking, graupel is not the same as hail or ice pellets, although it is sometimes referred to as small hail. However, the World Meteorological Organization defines small hail as snow pellets encapsulated by ice, a precipitation halfway between graupel and hail.
The term graupel is the German word for the described meteorological phenomenon. Its METAR code is GS.
And, indeed, if you Google "graupel" and then "images", you'll find some with the overgrowths like I was seeing above. Mystery solved, thanks to Mr. Lockwood!