^^What nrhareiner said.
To knowledgeable people seeking a high quality horse for a particular discipline, they are very important when selecting yearlings.
The general rule of thumb is the more specialized the discipline, the more imortant the bloodlines. Cutting is a very specialized discipline requiring an overall conformation and ability that is different than "just" a Quarterhorse. Racing TB's would be another example of highly specialized horses.
As someone has already said, the proper bloodlines, and the proper mix of bloodlines, greatly improve the odds of producing a high quality horses. But they do not guarantee it...