In the original unedited shot, the shadows completely obscured our toddler's eyes and nose. Unfortunately, the 'snow' was falling for only a brief moment, so it was only after it was too late when I discovered my error.
Solutions (probably most ideal to least ideal):
1. Off-camera fill-light. The ideal solution is to use another off-camera light source for fill.
2. Increase the size of the light source by bouncing it or using a modifier (e.g. umbrella). A larger light source can wrap around obstructions to some extent, and is less likely to create shadows that completely obscure large parts of the subject.
3 (tied). On-axis fill light. If you're using the pop-up flash or an on-camera flash as controller for the off-camera flash, the problem can be minimized by using the pop-up flash or controller as a fill-light (dial in -2.0 or so flash exposure compensation). The trade-off for Nikon CLS users is that you're precluded from using an SG-3IR to reduce blinking from subjects.
3 (tied). Balance ambient. The ratio of flash to ambient can be balanced more carefully so that there's enough ambient to act as fill.
5. Postprocessing can help but only to some degree, as the shot above shows.