I don't think you can call it a "minor "dynastic struggle jno. It was a war that lasted for about 30 years and saw some of the bloodiest battles ever fought on British soil.
In particular, there were more than 20,000 people killed at the battle of Towton - out of the 50,000 (or more?) men who participated in it. As the population of England at the time was only about 5 million, that's at least 2% of the entire male population participating in the battle. There was an interesting documentaryt on TV about this batttle a few years back: amazingly, they're still finding bodies from the battle.
Wikipedia has a good section on the Wars of the Roses.
http://en.wikipedia.org/wiki/Wars_of_the_Roses
A few years ago, the RSC did all eight historical plays, one after the other, and it was possible to see how a struggle over the crown has its roots in an event many years earlier. Shakespeare was an arch Tudor propagandist so he's a bit biased against the Yorkists and he also concertinas events together so it looks like things happen just after each other when, in reality, they were several years apart. But it's still fascinating to look at history through his eyes.