Greyjoys Vs Arryns

[Free Northman Reborn]

The Ironborn aren't going to conquer any mainland kingdom in a one on one war. They may sack a town or two, and raid some coastlines, but they don't do siege warfare and don't have the numbers to besiege any great fortress or city for any length of time without being crushed by the superior land forces of the enemy.

Harren's grandfather conquered much of the Riverlands, but he did so gradually over many years, at a time when the last of the Riverkings had been killed centuries before by the Storm King.

So the Riverlands were divided and Harren's ancestors were able to conquer one Riverlord at a time, assimilate his holdings into their growing empire and then move onto the next one.

This will not be possible against any full kingdom in Westeros.

It is quite simple. The Ironborn can strike at small parts of a kingdom, and wreak some havoc, but they can never actually conquer any of the other kingdoms. Historically, they have always been repulsed in the end.