EDIT: found the map

Well, to be perfectly clear the 'Roses' of the Wars of the Roses were not really the counties. They were at times used as badges relating to the Dukes of York and Lancaster. Both of these Duchies were vast and covered a great deal of territory that was nowhere near those areas, a system that happened with most if not all major nobles, so that they wouldn't have all their stuff in one easier to defend block. AJ Pollard had a really clear map demonstrating this in his book on the subject, but I can't seem to find it online (I'm getting lots of maps showing where battles were, which doesn't help much at all).

Not only is this not a story of two counties, but the holders of both duchies wouldn't necessarily have spent most of their time in those two counties. Richard of York (York) was at times the Lieutenant of Ireland and spent a great deal of time there. Henry VI (Lancaster) was, of course, the king, and parliaments were held in a number of different cities.

I would then suggest that the wars didn't start out of any animosity between Lancaster and York, but out of the personal displeasure of Richard of York with his king, Henry VI. To summarise briefly: Richard of York tried to force his way into the top position on Henry's council, and failed. He then got it when Henry VI went mad. He then lost it. He then declared himself king, and brokered a treaty where he was made heir to Henry. During all this, he killed several of his most important noble rivals, and was then himself killed.

It was then the sons of these leading nobles, by and large, that continued the blood feud, in part because of belief of royal claims, in part to advance their own status, and in part because other people were willing to help them to engage in private vendettas. But I've read nothing to suggest that it was really fought because people in the two counties disliked each other.

I know this doesn't answer the question fully and doesn't explain how and when animosity might have developed, I just want to explain that it was almost certainly irrelevant to the course and cause of the wars, and therefore may well not have related to their practical effects on the people in them.

AJ Pollard, The Wars of the Roses

David Grummitt, The Wars of the Roses