Hi shilpinator, welcome to SMC, I hope you'll enjoy your stay here.
About boolean modifiers, I'm not a Rhino user, but I think booleans are useless in almost every single 3D software : they almost always create terrible mesh, and you'd better go for modeling the tire by yourself, it's not so hard. Once I wrote a tutorial about it :
Pixels or Atoms ? It was written for Blender, but pictures are self explanatory for being used for any other 3D modeler.