Rickon misses the days he could just run in the snow covered woods with Shaggy. He misses Osha and Bran. And Jon too, he supposes, but everyone else in his family are strangers to him. They left him before he could even begin to remember them so he doesn't understand why King Stannis is so cross with him about Queen Arya Stark Targaryen. Intellectually he knows that she is his sister, that she is part of his pack, but he can't summon the feelings required.
Bran is still pack even if he hasn't seen his brother in years, he talks to Rickon in his dreams and tells him all kinds of interesting stories and teaches him to warg with Shaggy. Rickon knows he will never be as good a warg as Bran but Bran can warg with Heart trees. Bran is the closest thing to the Gods Rickon has and Godswoods have Heart trees and Bran can see through their eyes so Rickon supposes he keeps the old Gods, to King Stannis' annoyance.
Rickon remembers the day Osha died. It was after King Stannis' men had found them on Skagos and forced them to leave Skagos. They had just reached the shore of the Seven Kingdoms and they had fallen into an ambush made by the Others. Osha and the men had fought, Shaggy guarding Rickon, when Osha had shouted at the men to "take the littlest lordling" and run before she started chanting under her breath. He had kicked and screamed and bit but the man carrying him hadn't let him go, even when there was an explosion of fire behind them. Rickon later learned from other Free Folk that it was spell taught to everyone with even a drop of magic in their blood so that should they ever be in a situation like Osha's they would at least take the Others with them when they fell.
That night was the first night Bran came to his dreams. Rickon had known it was a dream because Bran was walking and in waking world Bran's legs were broken and the big man had to carry him around on his back. Bran told him Osha was now in the weirwood trees and if he ever wanted to talk to her, he should find a weirwood. It wouldn't matter if it was a Heart tree or not but Osha would be able to answer him through a Heart tree. Father too, Bran added, but not mother. Mother had kept the Seven, he explained, and for that she went somewhere else when she died.
Bran had told Rickon not to tell anyone he, Bran, was still alive, that he would announce it himself when the time was right. Rickon hated Bran for that because that meant Rickon had to learn to be a Lord, a kneeler who had kneelers of his own but still knelt for someone. He didn't understand why. Robb, his oldest brother, had been King in the North, the head kneeler, so shouldn't he be King in the North too? Well, Prince in the North since Bran was alive but he wasn't supposed to tell that to anyone, but he would have knelt for Bran because Bran was so wise.
Jon visits him every once in a while, when the fight against the Others allows it, bringing Ghost with him. Rickon wouldn't have trusted him had he not had the direwolf and had Bran not told him about Jon but after meeting his dark haired brother, he is happy enough to include him in his pack.
So yes, Rickon is unhappy to ride south with King Stannis' envoy to Queen Arya who is and isn't pack. He doesn't care he has to ride in snow and endure the cold, that he is used to, but Bran told him he couldn't visit his dreams once he was south of the Neck because there were no weirwood trees for him to travel through. Once at King's Landing Bran would visit him again because there were some weirwood trees in the gardens but there was no Heart tree so Rickon couldn't talk to Osha or Father and Bran couldn't see what was happening. Rickon insisted that Bran tell him how to make normal weirwood trees into Heart trees so that Rickon could make Bran eyes in King's Landing and after continual begging for a fortnight Bran told him. Rickon gathered what he would need to make a Heart tree but grumbled to everyone in Deepwood Motte who talked to him about the journey.
He would make it, if only so that Bran would have eyes in King's Landing.