Daenerys could be an ally. Since she is the mother of dragons, she might initially be hesitant but then see the potential in Jon Snow riding one of her dragons. They could team up to fight their common enemies.
In a fanfic where Jon Snow rides a dragon, he would gain several new abilities. The ability to fly, of course, is a major one. This would allow him to have a better view of the battlefield, plan strategies more effectively. The dragon's fire could be used to burn down enemy fortresses or large groups of foes. Also, the dragon itself is a symbol of power, so Jon would gain more respect and fear from others. He could intimidate his enemies just by showing up on his dragon. Moreover, the bond with the dragon might give him some kind of telepathic connection, enabling him to control the dragon more precisely.
Hong Xixiang was one of the characters in Sword Snow Stride ". He liked to ride the green bull upside down. He cultivated the Supreme Heavenly Dao and was highly expected to become the representative of the Martial Dao Heavenly Dao. Hong Xixiang rode an ox to study for twenty years. One day, he came to his senses. He walked on a crane and became an immortal on the land. He had once snatched the horsetail whisk from Qi Xianxia, the Sword Chief of Taoism. He admired Xu Zhihu, but he did not dare to go down the mountain to look for her. Hong Xixiang was reincarnated as the boy Yu Fu and was brought back to Wudang Mountain by Li Yufu. He was the reincarnation of Ancestor Lu, and he used the reincarnation of Jun Jie to exchange for Xu Zhihu's ascension. He was willing to prove dao for the human world for another 300 years. Hong Xixiang's martial strength had reached the Celestial Realm on land.
If Jon Snow rides a dragon in fanfic, it would be a game - changer for power dynamics. Dragons are extremely powerful weapons in the Game of Thrones world. Jon, being a noble and a good fighter, would be able to use the dragon to his advantage. He could easily overpower his opponents. This would make him a key player not just in the fight against the White Walkers but also in the political struggle for the Iron Throne. It might even lead to him uniting the kingdoms more easily as people would be in awe of his dragon - riding ability.
Jon Snow could potentially have allies like the Mormonts. They have always been loyal to the Starks. Maybe even some of the Dornish houses might side with him. They have their own reasons to oppose the current power structure in Westeros. And of course, his friends from the Night's Watch who left with him or believe in his cause could be his allies in this conquest. He might also gain the support of some of the maesters who see the value in his leadership for the future of Westeros.
Daenerys Targaryen could be one to help. Since she has experience with dragons, she could give Jon Snow advice on how to care for the egg and hatch it.
It could be a young and untainted Frey. Maybe a niece or a cousin of the more infamous Freys. One who has not been involved in the past atrocities committed by her family and has a more noble heart.
Daenerys Targaryen is often paired with Jon Snow in such fanfictions. Their combined power and the potential for a different kind of relationship makes it a popular choice among writers. Another character is Arya Stark. Their sibling bond can be explored in new ways when Jon is reincarnated, like Arya helping Jon with her assassin skills in a different plot line.
The North would surely support him. They have always seen him as one of their own and a great leader. Also, the wildlings might back him, considering he has a history of working with them and understanding their plight. Davos Seaworth would most likely be on his side as well, given his loyalty to Jon in the past.