I'm imagining some hacked up workflow that includes:

- Something like Autodesk 3D Studio R3/R4 (DOS) or Lightwave 3D (Amiga) for the base animation and the light rendering - that would be hellish to do manually.

- Some custom-built software for palette optimization

- Photoshop on Mac for the compositing (the 'N' doesn't change)

- A bunch of manual work per frame

Not necessarily in that order.

(3d Studio Max was released in 1996, Maya in 1998.)

Edit: on the other hand: Netscape was founded and founded by Jim Clark (of SGI fame), so the 3d stuff was probably done on software running on an SGI machine.