There are a few things that make it possible to tell the difference.
And in true definition, it reigns pretty true (viaDifference Between).
Cuddling is usually suggesting more of “handling,” and using your hands.

It can lead to more sexually intimate moments, as well.
Snuggling, on the other hand, can be seen as more platonic.
Think of snuggling with your grandmother, or even with your own children and pets.

Snuggling involves far less movement and often times includes “burrowing.”
As with any words though, the definition is really in the interpretation.
So, it all depends on who you ask and who you talk to.