Line large sheet with parchment or silicone mat.
Crush candy canes into small pieces in zip-top bag with rolling pin; kids can help.
Microwave white chocolate and oil in microwave-safe bowl in 30-second intervals, stirring between, until melted and smooth.
Pour chocolate into tall glass or mug for dipping.
Dip rods about 2/3 into chocolate; drain excess.
Immediately add candy canes, rotating to coat all sides.
Place on sheet; repeat with remaining pretzels.
Set 30 minutes at room temperature or 15 minutes refrigerated.