I think the problem in trying to find a military commander in the North is that they are fighting a completely different enemy than the rest of Westeros. They fight for reasons that are far different than the other Houses, be they small or great.
In the North, when the cold winter comes and food grows short, the elder men of a family or House will say they are going to go "hunting" and will return when they have something. Everyone knows this is false. This is the Northern way of cutting down the number of mouths to feed when winter comes. To go "hunting" during the winter is to go out and die in hopes of saving food that could save your family. No other place in Westeros has to contend with the cold as much as the North does. They base their entire LIVES around this season.
Ironically, it's the cold that also gives them their power, for no other men are able to endure the drifts and snows of Winter like the Northerners can. During Stannis' March on Winterfell, it's said that the Northern Houses who rallied for Stannis were able to fair much better in the snows than Stannis' southern troops.
The North are a practical and pragmatic folk. They don't wear fancy clothes because fancy clothes are usually made out of silk and in the North, silk is useless. For this reason, they value furs, wool, and animal skins to keep them warm. Moreover, they think jousting is stupid. To them, the point of fighting is to kill and win, not brag and prance around in glory.
The reason there appears to be a stigma in terms of military intelligence and leadership in the North is that their main campaign involved declaring Robb Stark King in the North...and then riding south. Past Moat Caillin, there is no place for a Northern army. They do not have the numbers, nor the technology to effectively wage war against any of the Houses in the South. Sure, Robb won every battle against Tywin Lannister but Tywin Lannister had 20,000 men to himself plus another 14,000 commanded by his brother, Kevan as well as a 3rd army being formed up in Lannisport; not to mention the fleet of Lannisport. Robb Stark, our King who Lost the North, only had 20,000 men. That's all he ever had. The Battle of the Whispering Wood may have captured Jamie, but it cost Robb 2,000 men. The losses for the North weighed much much harder than the losses for any Southern Houses.
While 20,000 may seem small compared to the massive armies fielded by say, Highgarden, keep in mind of just how big the North is. It's as big as all the other 6 Kingdoms combined. There is no effective way to enforce and govern all of the North, which means a lot of what Northerners do comes down to loyalty. Those 20,000 men who followed Robb, while they were a small force, were willing to follow him to the ends of Westeros if need be. We can leave out the Boltons and their treachery given their centuries blood-feud with the Starks and the Karstarks for Robb's mistakes. The North doesn't forget what the Starks did for the Manderlys, or the Wulls, or the Flints, or the Liddles when the cold winter came. The North doesn't forget that the Starks and Winterfell were the reason many of the Northern Houses even survived many cold winters. The North doesn't forget their allegiance to the Starks. The North Remembers.
We are susceptible to believe the North doesn't hold any great commanders, but then you look back and realize that they all did one thing wrong ...they rode south. King Torrhen Stark went south and bent the knee. Rickard went south and he burned for it. Brandon went south and choked himself to death. Eddard went south and lost his head. Robb went south and lost a kingdom. When the Starks (and the North) go South, they fail.
But in the North, each Lord becomes a commander in his own right. Rarely do the Houses in the North come together unless winter approaches or the banners are called. For this reason, the Houses tend to keep their armies at home. They learn the land and understand the terrain. Each House knows every rock and every tree that they govern. Given this knowledge and their resistance to cold, any foreign army would have an extremely difficult time trying to conquer here. This is the North's hidden strength. Here, in the vastness of the wild, in the wide plains and valleys, in the endless fields and towering mountains, reside the Lords of the North, who are ruled by their liege lords, the Starks, the Kings in the North and the Kings of Winter.