To explain some aspects that have confused others: this story is partly (mostly, so far) a comedy that relies at least somewhat on how it mimics traditional Chinese/Korean/Japanese historical romance novels.
In this sort of traditional East Asian monarchy, the Emperor is the ultimate power in the realm. The emperor's first wife is known as the Empress. The emperor's mother (who is almost always the former empress and widow to the former emperor) is known as the Empress Dowager. Both the empress and empress dowager are treated with extreme respect because they are considered to have the ear of the emperor.
It is a very common belief of those times that women (especially powerful ones) would lead their husbands towards certain conclusions or ways of thinking on matters of state that they felt were important. This wily or manipulative behavior is part of how we think about these monarchies. It is one of the reasons that fictional emperors are often naive or incompetent, and fictional empresses and empress dowagers are often scheming and villainous.
Additionally, there exists an imperial harem. Its rules and responsibilities are even more complicated and tend to vary more between stories. Relevant to this series is the knowledge of a few terms relating to the harem. The term "rear palace" (seems to be called "forbidden palace" in this translation, which is a term for it I was not familiar with - probably places this series in ancient China at the Forbidden City) refers to any palace where the imperial harem and/or Empress Dowager are housed. The exception is that any women housed in palaces that are unfavored by the emperor are known as "cold palaces".
To answer the speculation above, yes, the Emperor is pretending to be male, and most people are likely not aware of the ruse. If I had to guess, I would guess a specific selection of palace staff know as well as the empress and empress dowager. Although she dresses in a what we interpret as a feminine manner during the day, this is actually crossdressing for the time period. Long hair, held up by hair accessories like you noted, and robes were common garments for men of noble birth back then (and eunuchs, but that's a different topic). Likely how it works is that she's the emperor by day, then switches into feminine clothing and goes into the "cold palace" for the night.
This is a source of some of the humor and tension because our MC thinks the "pretty sister" is in the cold palace because she is out of favor with the emperor. She decides this means that she can badmouth the emperor without repercussions and proceeds to do so, unaware that she's insulting the person to their own face.
It's very unusual for this style of story because usually a lot of the conflict is the MC getting along with the empress, empress dowager, head eunuch, or the emperor himself (herself). However, our MC has found herself in good graces with almost all of those people so far, and her only real enemy is her own ignorance of the emperor's true nature. It's a good twist for a GL story.