There seems to be a trend with the oldest civilizations (Civilizations being urbanized societies with a government and social heirarchy) starting around river valleys surrounded by desert; the Egyptians, Sumerians, and Harappans as examples. The issue is, they are all located around a hot desert climate. While our Earth as we know it today has no major rivers flowing through a cold desert, my constructed world has plenty, so it'd be essential to know if that was possible. My research in this hasn't yielded many answers, and the only thing that I've really found is that parts of the Yellow River flows through a cold steppe. This isn't really helpful to me though, since I have large rivers going through large cold deserts in my constructed world. Basically, my question is if a civilization could develop on its own around a river valley in a cold desert climate. I apologize if the answer should be obvious to me. This is assuming a technology level similar to the ancient Egyptians or the Sumerians around 2500 bce.
Ancient civilizations flourished around rivers in warm (Mesopotamia) or hot (Egypt) climates because the combination provided excellent conditions for agriculture.
But we do have ancient(-ish) civilizations which developed around rivers flowing through cold deserts.
The entire Transoxiana, the strip of land between the Amu Darya (formerly Gihon, formely Oxus) river and the Syr Darya (formerly Seyhun, formerly Jaxartes) river is a cold desert, part of the Kyzylkum desert, the Red Sands. Transoxiana has a long and fascinating history.
On the same river lies Bukhara, another ancient city with a resplendent history.
To the north, on the banks of the Oxus, lies the splendid oasis of Khwarazm. It was the birth place of Muhammad ibn Musa al-Khwarizmi, author of the pivotal Book of Calculation by Completion and Balancing; medieval Europe called him Algorismus, and translated the title of the book as Liber Algebrae, using the Arabic al-jabr "addition" or "completion". A civilization which gave us both the word "algorithm" and the word "algebra" was definitely important.
What is true is that while all these civilization appeared and endured using the resources of their cold deserts and mighty rivers, the actual thriving was due to trade. In the case of the examples given, the trade was the trade on the Silk Road: the Tarim Basin, Samarkand and Bukhara are directly on the Silk Road, and Khwarazm, a little to the north, was a major supplier of provisions and trade items.
Yes, we do have old civilizations which appeared and endured on rivers flowing through cold deserts.
Remember that a cold desert usually has warm summers, exactly because it is a desert. (Unless it is located in a frigid zone, that is.) Warm summers plus river make for good conditions to practice agriculture. The cold and dry winters are a great incentive to organize a civilization!
A large river valley is almost certainly the only location in a cold desert climate ecosystem where a civilization of any type could develop. There are two problems, the first of which is water. For civilizations to develop you need a location that is fertile enough and well irrigated enough to support a significant population for an extended period of time (multiple generations) in a relatively sustainable/consistent manner i.e. more average to good growing years than bad ones. And the local climate along the length of a broad river valley should be less harsh/sustain a more complex ecosystem than the desert plains around it.
The second one is domesticated crops and animals. Your culture would have to have access to at least a limited range food crops, root vegetables, grains, fruits, gourds, leafy greens etc and domesticated animals. The latter is probably not as much of an issue because cold deserts can and do a support nomadic herdsmen and hunter gathers. So your culture can inherit a tradition of animal husbandry.
The crops are another issue. I'm more than happy to be proven wrong but as far as I am aware cold desert environments don't naturally host a wide range or variety of traditional food plants. That means any crops (and you will need crops) have to be either cultivars of wild plants found growing naturally in the valley when the original settlers arrived generations ago or else be traded 'up' river or across the desert from other regions where they do grow naturally.
Your river valley doesn't have to be a 'Garden' of Eden' in terms of all the varieties of crop plants grown there but you will almost certainly need at least half a dozen different crops across a wide range of types to produce healthy/balanced diet for your citizens.
You might look at some of the crops grown by ancient South American peoples as examples of what could be grown in different climate ranges.
Cereals crops are must
Any civilization needs cereals crops to survive.
Freeze injury of rabi or winter cereal crops
Wheat, oat, barley, gram are winter crops.
If at heading and flowering stage, the temperature goes below 0°C, the crops are severely damaged as explained here.
Suitable temperatures for kharif crops
Rice, maize, millet are kharif crops.
As explained here, they are grown where:
The average temperature during the growing season is between 20°C and 27°C.
Sunshine is abundant during their four months of growth.
The minimum temperature does not go below 15°C as germination cannot take place below that temperature.
Such cultivation conditions are not present in cold deserts.