Line a baking sheet with parchment paper and set aside.
Place the pecans and shredded coconut in a food processor and pulse until the pecans are finely ground.
Add the pitted Medjool dates, coconut oil, sea salt, and vanilla extract to the processor, then add the arrowroot (or tapioca) starch; process until a sticky, cohesive dough forms.
Scoop level tablespoonfuls of the dough (or use a small cookie scoop) and roll into balls; place them on the prepared baking sheet.
Freeze the balls on the baking sheet for at least 1 hour to firm up.
Put extra arrowroot powder in a small bowl and roll each chilled snowball in the arrowroot to coat.
Store the coated snowballs in an airtight container in the refrigerator.