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Boolean operations may give problems with polygon models, but they work like a charm in NURBs apps, like Rhino (or StudioTools, Inventor, SolidEdge and others).
You can have those tire treads done in many different ways. A common practice in Rhino is to build a single tread pattern, then (one dimension) array it to get the total number of strips pr treads of the tire, and finally use the bend tool (360 degrees to get a perfect cylinder).
There are many other ways though, like using pure booleans, like you are doing. You may continue with that approach, making the boolean operation with less geometry selected, repeating as necessary and deleting unwanted remaining geometry.
As an example, the geometry showed on pic is a pattern bended to a surface.
Good luck!
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