The key was absolutely fireplaces. The Duchess of Orleans at that time, Elisabeth-Charlotte von der Pfalz, has a steamingly gossipy letter collection. In one of them, she complains about how much Versailles absolutely sucks and why can't she stay at one of her own palaces all year round. Oh, right, because they don't have fireplaces in all the apartments and her servants would freeze to death. Well, maybe they could just freeze...

During this era, "footstoves" or fancy boxes with heated coals in them were also popular for personal use in large cavernous rooms (think churches). But overall, it's important to keep in mind that the function of indoors in winter was less about the room being warm and more about it being dry (because then you could warm up, e.g. by wearing more clothing or sitting by the fire--although the latter wasn't always good enough; the Jesuits in New France talk about being unable to write because their ink had frozen in the inkpot even right by the fire).

Heating was a problem in Versailles. Well everywhere to be honest, in castles of course and for other people as well, no matter the modesty of the house. Castles are generally known difficult to heat and Versailles, because of its size, is impossible to heat.

There are several accounts of people complaining about the difficulty of staying warm in Versailles and the general discomfort of the palace. As u/sunagainstgold mentioned, the sharp-tongued Princess of the Palatinate did not restrain herself from making comments. All sorts of technics were used to try to stay warm such as spending winter cloaked in a bear skin, carrying hot water bottles, footstoves ...etc Apparently, King Charles Spaniels are popular dogs among the ladies because they are a kind, cute source of warmth.

To answer your question, not every room had a fireplace, far from it. Today, there are 352 fireplaces in Versailles. In 1789, an estimated 1,200 fireplaces existed. Fireplaces at the time are not very good at providing warmth. In the 17th/18th centuries, they are bigger than they used to be (big enough to have a human inside, it is the period chimney sweeps became an important job)? Bigger means a bigger fire but also more space for the wind, rain, and snow to come inside. In the last years of Louis XIV's reign, 6,740 people are housed by the royal treasury including around 4,000 inside the palace! In winter, this number is probably lower but it still means a lot of people lived in Versailles. As such, doors kept being opened and opened letting the cold air through. Another issue was the stench because so many people with questionable hygiene living in the same place caused body odors to fill the rooms. Added to other inconvenient smells like the smoke from the fireplaces, some of the 2,100 windows in Versailles are opened, even in winter, to let some fresh air in.

Louis XV is known to be bothered by the cold in Versailles. In his quest for privacy, the not-so-Well-Beloved king modifies the petit appartement du roi (the King's small living quarter) to be fit for living. The rooms are much smaller than the other living rooms and thus easier to keep warm. During winters, those who can leave Versailles tend to go to more comfortable places (such as a hostel in the city or their family estate).

EDIT: During the Great Frost of 1709 that devastated Europe and cause perhaps to 1,000,000 deaths in France (highest estimates), Versailles was also hit hard. Testimonies mention the king's frozen wine. The court could not make it to Marly, a chateau a bit more comfortable (Louis XIV's palace for friends).

The Duke of Saint-Simon has interesting things to say about this particular, exceptional event. However, harsh winters are common during Louis XIV's reign. Source:

One of the reasons Madame de Maintenon had brought forward, which much assisted her in opposing the siege of Lille, was the excessive cold of this winter. The winter was, in fact, terrible; the memory of man could find no parallel to it. The frost came suddenly on Twelfth Night, and lasted nearly two months, beyond all recollection. In four days the Seine and all the other rivers were frozen, and,—what had never been seen before,—the sea froze all along the coasts, so as to bear carts, even heavily laden, upon it. Curious observers pretended that this cold surpassed what had ever been felt in Sweden and Denmark. The tribunals were closed a considerable time. The worst thing was, that it completely thawed for seven or eight days, and then froze again as rudely as before. This caused the complete destruction of all kinds of vegetation—even fruit-trees; and others of the most hardy kind, were destroyed. The violence of the cold was such, that the strongest elixirs and the most spirituous liquors broke their bottles in cupboards of rooms with fires in them, and surrounded by chimneys, in several parts of the chateau of Versailles. As I myself was one evening supping with the Duc de Villeroy, in his little bedroom, I saw bottles that had come from a well- heated kitchen, and that had been put on the chimney-piece of this bed- room (which was close to the kitchen), so frozen, that pieces of ice fell into our glasses as we poured out from them. The second frost ruined everything. There were no walnut-trees, no olive-trees, no apple-trees, no vines left, none worth speaking of, at least. The other trees died in great numbers; the gardens perished, and all the grain in the earth.

I advise being careful with Saint-Simon however, as explained here his message is very political.

In January 1709 letters, Elisabeth-Charlotte von der Pfalz reports what she heard from what is happening in Paris. The cold killing the more unfortunate people she describes can also enlighten us on the temperature in Versailles.

On the 19th of January: It has never been so cold in men's memory [...].[...] we hear every morning about people found frozen. On 2nd of February 1709: In Paris only 24,000 people have died since the 5th of January.

Sorry for the long edit, I had to find Saint-Simon's quote in English. Of course, 1709 is not representative of every winters at Versailles. Far from it. Yet it shows that it is a very difficult thing to keep Versailles warm.