So, as mentioned before I ran through the House Creation rules and here's what I came out with for my house. Warning, there are numbers but I've done my best to explain what they mean relatively. I smoothed out the stats a bit since I won't actually be USING hard numbers in play and this was just a prompt to see what I could turn said numbers into.  

[hider=My Hider]
Realm: The North
Defense: 30 - Defensible, at least one fortified town or castle
Influence: 50 - A powerful minor house with colorful history, equivalent to House Florent or House Frey
Lands: 50 - Significant lands across many miles.
Law: 17 - Lawlessness and banditry are a problem
Population: 21 - Typical; farmsteads and hamlets mostly, maybe a couple of small towns
Power: 20 - Small force of soldiers, primarily smallfolk
Wealth: 25 - Common; enough to get by and some small luxuries

Age: Ancient (Age of Heroes)
Founding Event: Catastrophe 
Historical Events: Villain, Ascent, Infrastructure, Scandal, Infrastructure
Most Recent: Conquest

Holdings: Small Castle
Children: 3 sons, 2 daughters.
Lands: Plains (Small Town, Road), Hills (River)
Military: Trained Garrison, Trained Cavalry, Green Peasant Levies, Trained Infantry
Wealth: Godswood, Maester, Marketplace  
[/hider]

Now, here's what these events mean: given that they were founded due to an ancient catastrophe in the North, I'm thinking they were established in the wake of the Long Night. There once was a brave Northern king, let's call him Orrick, who gathered his men to him in preparation of the coming winter behind his castle's high walls. When the snowfall stopped and no word came from Grey Bastion or the men within, the surviving First Men found the gates bolted but the castle wholly empty. All the men within seemed to have entirely vanished, women and children too. Orrick had gathered his family close and they were nowhere to be seen. Ownership of Grey Bastion was claimed by Caer "Cruel-Ice" (our Villain event; he shored up the military and political power of the house at the expense of the smallfolk) Let's say that it's from him the house takes it's name; House Caerson. 

For the most part, House Caeron has been quiet and working hard at the business of living and staying out of political squabbles (the Infrastructure events). They fought off the Ironborn during their Ascent. During the Conquest, there was a Scandal - given that Torrhen was marching south, perhaps Caerson refused to march and even argued for the North to submit to the Targaryens. Most recently, during the Dance of Dragons, the House has prospered greatly; perhaps Lord Caerson was part of the Winter Wolves or kept the company of Lord Cregan Stark. Or perhaps there was more active conflict in the North during the Dance and the Caerson's crushed a Green house?