The stories of Liu Xijun (130-101 BC) and Liu Jieyou (121-49 BC) could be examples for your question.

Xijun was daughter of Liu Jian, Prince of Jiangdu, and a member of Han imperial family. At the time the Han Dynasty was seeking an alliance with Wusun people, who lived in nowadays northern Xinjiang and eastern Kazakhstan and would provide an excellent ally against the Xiongnu of Mongolian Plateau. Thus in 108 BC, Liu Xijun was married off to the Kunmo, or King of Wusun. The Kunmo made her his junior wife, while his Xiongnu wife held the position of chief consort. Xijun’s life in the northern steppe was recounted that: “Upon reaching the land [of Wusun], the princess had palace built to serve as her residence. Every year she and the Kunmo would held one or two banquets together, where they feasting in wine and awarding the king’s ministers with silk and precious gifts. However the Kunmo soon grew old and unable to communicate anymore. In her lamentation, the princess wrote a song that said:

'My family married me off to the edge of the world. Far away in the strange land of the king of Wusun. A domed hut is my chamber, the felt my walls, Meat is my food, fermented milk my broth. The constant longing for home makes my heart ached. I wish to become a golden crane, returning to my homeland.' ” (Book of Han, Vol. 96, The Account of Western Region)

After Xijun’s husband died, his nephew became the new king and wished to marry her, according to the levirate custom of steppe nomads. Xijun protested against this at first, but after receiving order from the Han emperor, she reclutantly complied.

When Xijun died, the Han again sent a new bride for the Wusun - Liu Jieyou. Princess Jieyou’s grandfather had previously rebelled against the emperor, and her low status made her a suitable match for the “barbarian” king. Jieyou would go on to marry three Kunmo, and heavily involve in Wusun politics. In 72 BC, her letter to the Han emperor brought a large Chinese army to help the Wusun against Xiongnu attack, and ultimately curtailed Xiongu influence in the west. Jieyou later conspired with several Han officials to overthrow her third husband, king Nimi of Wusun. While her plot was a failure and Jieyou barely escaped with her life, the coup set the stage for internal division within the Wusun, creating two groups ruled by a Greater Kunmo (who was Jieyou’s offspring) and a Lesser Kunmo respectively. At the age of 70, Jieyou was allowed to return to the Han and was welcomed grandiosely by the emperor. She passed away two years later in 49 BC.

From these informations, we can imagine how the lives of Chinese princesses in the northern steppe would play out. The abrupt change in life might be a shock at first, and homesickness would always remain, but as highborn ladies and relatives to the emperor of China they were certainly offered the best living standard among the nomadic peoples. And while there wasn’t much opportunity for women to pursuit in such patriarchal societies, some had taken on more active roles beside the traditional housewife one, using their connection to influence the politics of northern steppe, even making important outcomes themselves, as demonstrated by the case of Liu Jieyou.

(Sorry for not being able to provide English source, since I took this directly from the "Book of Han")

The comment above is already superbly detailed, but I would like to just add some clarifications on the broader picture of Ancient China's policy of Heqin 和亲 aka. marrying princesses to the "barbarians". The practice of Heqin started in Han dynasty (202 BC – 220 AD) and was continued all the way until the Qing (1644-1912). Throughout the mellenia, different Chinese dynasties conducted it differently with different groups of "barbarians." As always, the reality of the situation is much more nuanced than simply "Chinese princesses ending up in arranged marriages to steppe warlords."

First, the stories of Liu Xijun and Liu Jieyou, while famous, are not representative of the majority of Han Heqin princesses—because, surprise, the majority of those "princesses" weren't actually princesses at all! The Chinese traditionally looked down upon the nomadic tribes to the north, and while geopolitical pragmatism forced the adoption of Heqin policy, it was still considered quite humiliating to essentially marry off women to sue for peace. You can find plenty archival records by famous Confucian scholars lambasting Heqin as a political and moral failure (cf. Zizhi Tongjian, Chapter 12, Han vol. 4). And the Chinese emperors at the time weren't stupid either. Very rarely were actual members of the imperial family married off. In the first ever case of Heqin by the Han dynasty in 198 BC, the Chinese court simply picked a random lady-in-waiting (家人子, essentially a maid) and married her off to the Xiongnu, telling them that she was the grand princess. The most famous Heqin "princess" in Chinese history, Wang Zhaojun, one of the "Four Beauties" in Ancient China, was also like this. She was simply a maid in the imperial harem—the Emperor never even saw her or really knew who she was before sending her away. Wang was still amongst the lucky ones though, at least the official histories kept a record of her name. Most of the time we don't even know who those "princesses" were, where they came from, or who were their parents. The official Han court histories simply referred to them as 宗女刘氏 (imperial lady of the Liu family) and the Xiongnu referred to them as 阏氏 (wives). How did they fare? What did they think? The true stories of those women are forever lost to the annals of history, silenced by the archives.

Of the entire Han dynasty, only Liu Xijun and Liu Jieyou were actually real princesses, and then only of the extended imperial family. The Tang dyansty (618-907 AD) also practiced Heqin, initially following a similiar strategy of pretending random maids as princesses (scamming the barbarians, basically). But, after the An Lushan Rebellion, the Tang empire was pushed to the verge of collapse. In a desperate attempt to secure an alliance with the Uyghur Khaganate to turn the tide, Emperor Suzong actually married off his own daughter to the Uyghur Khagan (who in return married his daughter to a Chinese prince). Because of this dramatic precedent, Heqin princesses of the late-Tang dynasty were all real princesses. Other than the Uyghurs, the Tang also conducted Heqin with the Tibetans, the Jurchens, Nanzhao, and Korea. These peoples were not at all steppe warlords, and the Chinese brides certainly did not have to live in yurts. If anything, Heqin marriage might even had been an opportunity for them, as they had transformed from nameless ladies-in-waiting into actual queens wielding political power.

The Northern Song dynasty (960–1127) preferred to wage total war against the nomadic peoples, so naturally Heqin was out of the question. By the Southern Song dynasty (1127–1279), however, a severely weakened Chinese regime was forced back into the practice. The Ming dynasty (1368-1644), having ended the Mongol yoke, carried some serious nationalist/revanchist sentiment, and steadfastly refused to settle for peace with the northern "barbarians." By the Qing dyansty (1644-1912) the Heqin dynamic was completely different, as the Manchus themselves were of "barbarian" origin. Qing China used Heqin extensively as a strategy to unify the various ethnic minority powers within the empire. But by then the Manchu, Mongol, Tibetan, and Han Chinese peoples were already highly integrated in society—a Mongol prince receiving a Manchu princess probably had three courtyards in Beijing himself. So life was, probably, just normal.

In conlcusion: Heqin 和亲 was a nuanced and complicated practice that evolved and transformed over the centuires. It's hard to generalize its entire history with one or two stories. Most Chinese princesses in the Heqin system were not actually princesses, and most of them also did not have to live in yurts.

Source: 中国古代和亲史 [Heqin History of Ancient China], Cui Mingde, 2005.

Thank you so much for the answer. It does seem like a pretty drastic change, but I imagine it could offer additional opportunities as well.