I’m surprised that...

[Nevets]

According to Maggy, Robert has 16 bastards.  Varys says he knows of 8.  The readers know of 7, and the only one of those Varys might be unaware of is the girl at the Peach in Stoney Sept.  That means that the vast majority of remaining bastards are unknown to Varys, which means they are probably unknown to anybody else as well.  Certainly Robert; and possibly even their mothers.  It is possible that some of these are in the North.  In any event, it hardly matters.

As to why none of the known ones are from the North, it is probably lack of opportunity.  It is hard to father bastards in a location you rarely visit.

[Melisandre's Rubies]

 

From the conversation Robert and Ned have, right after Robert's arrival in GoT, this seems like his trip to Winterfell and the North.

Quote

"I trust you enjoyed the journey, Your Grace?"

Robert snorted. "Bogs and forests and fields, and scarcely a decent inn north of the Neck. I've never seen such a vast emptiness. Where are all your people?"

"Likely they were too shy to come out," Ned jested. He could feel the chill coming up the stairs, a cold breath from deep within the earth. "Kings are a rare sight in the north."

Robert snorted. "More likely they were hiding under the snow. Snow, Ned!" The king put one hand on the wall to steady himself as they descended.

"Late summer snows are common enough," Ned said. "I hope they did not trouble you. They are usually mild."

"The Others take your mild snows," Robert swore. "What will this place be like in winter? I shudder to think."

 

He specifically says that he's never seen "such vast emptiness" and by his description of the journey it doesn't seem like he's experienced any of those places previously.  

The two years leading up to the False Spring in 281 were during winter and Robert can't conceive of what it would be like during winter, which means he wasn't there during that time. The False Spring was very short and the Tourney of Harrenhal took place during that time period, meaning Robert, along with Ned, Lyanna, Brandon, and Benjen, were down in the Riverlands during that time. Even then, then it only says that the snows were melting not absent. 

Quote

In the annals of Westeros, 281 AC is known as the Year of the False Spring. Winter had held the land in its icy grip for close on two years, but now at last the snows were melting, the woods were greening, the days were growing longer. Though the white ravens had not yet flown, there were many even at the Citadel of Oldtown who believed that winter's end was nigh.

The False Spring of 281 AC lasted less than two turns. As the year drew to a close, winter returned to Westeros with a vengeance. On the last day of the year, snow began to fall upon King's Landing, and a crust of ice formed atop the Blackwater Rush. The snowfall continued off and on for the best part of a fortnight, by which time the Blackwater was hard frozen, and icicles draped the roofs and gutters of every tower in the city.