Why was the northern boundary of the Mongol empire set where it was?

Post number 14 at Historum, and the posts which follow it, suggest that the Mongol Empire extended much further north into Siberia, and was much larger, than it is usually depicted on historical maps, and perhaps was actually larger than the British Empire.

So possibly the correct answer might be that the northern border of the Mongol Empire was not where you think it is, but much farther north, possibly reaching to the Arctic Ocean everywhere in Siberia.

This article looks at conceptualizations of the surface area of the Mongol Empire and notes a potential problem: The Mongol Empire may not have actually had a northern border in many parts and it is not always clear how modern researchers have established the border that appears in modern map-depictions. This article looks at three issues: the background of such map-depictions in modern historiography, the primary source evidence for the northerly limits of the Mongol Empire, and the Mongols' own stated imperial ideology. The conclusion of this article is that the Mongol Empire's true and claimed extent of territorial ownership and authority is not being accurately depicted on modern maps of the Mongol Empire. Indeed, taking into account certain perspectives, it could be reasonably argued that it was the largest empire in history. Researchgate.net

Mythical answer: Ignach Cross stopped them from going north.

To answer this I would first answer the question, why did Orda retreated from Hungary and central Europe. As the guy named Lord of Hosts explained in his "articles" there were, and still are, economic reasons that contributed to mongol success and their failure. And by economic I don't mean financial only; in fact I don't mean them at all. Economy is not only about currency and money. Just like one economist calculated that Jurassic sauropods needed to move 100 times a day to feed themselves, he utilised economy to do that. Same applies to horses. So to the point - economic laws apply to war as well. As explained in mentioned articles Orda was thriving on steppes, and grass fields, not in the forests. And the main reason for it is simple.

The key to Mongolian victory was speed, range and mobility. Without these the ordu would have been bogged down, encircled and obliterated by weight of numbers of the scope which only settled agriculture could support. The Mongols’ unparalleled success in steppe warfare required a string of remounts, often as many as eighteen. Horse-power required pasture, superabundant in the great pastoral belts of Mongolia, China, Russia and the Middle East, but almost non-existent in the dark forests and arable lands of Europe.

The Alföld — the great Hungarian plain — was the largest unbroken pasture on the continent of Europe, in fact the only one of any extent. It was therefore the main target of Batu’s invasion. Prior to urbanisation in the twentieth century, it contained some 16,371 square miles of pasture, barely sufficient to sustain 150,000 wiry steppe horses. So even had the herders restricted themselves to ten remounts, the Alföld couldn’t even have sustained two tüman: only 15,000 nomads against an active Western military reservoir of millions.

In theory, by accepting that five-horse limit, which still enabled 65,000 Mongols to spread their terror through the deserts of the Middle East, Batu Khan could have maintained on a permanent basis in Europe only three tüman or 30,000 troops, half the number that he had brought with him on his initial foray into Poland and Hungary, and only a fifth of the number with which he had crossed the Volga and overcome Russia, an empty steppe country with a pastoral economy suitable for nomadic warfare, and with only a tenth of the population and military potential of the West.

So, Mongols needed steppes, vaaaast steppes, otherwise they couldn't stay for long, which means if they couldn't conquer a territory in swift manner they couldn't conquer it at all. They were unable to besiege fortified settlements which were often in Europe, even Russia, and after first wave, people in Europe learnt to build fortifications and not fight in open fields. That's the reason why second invasion failed either in Hungary and in Poland - people were not willing to fight in open and defended in towns and castles, that were out of reach for the Mongols. Here, enough to say that on a later campaign it would take Hülegü three years to transport a thousand crews of Chinese artillerymen and their siege equipment two and a half thousand miles from the steppes of western Mongolia in 1253 to Khurasan in 1256, and another two years before they could topple the walls of Baghdad a thousand miles farther west.

And now back to Northern Russia - by the time, it was heavily forested country, that would not offer enough fodder nor food for long campaign. In his book Das Rätsel der Menschwerdung: Die Entstehung des Menschen im Wechselspiel der Natur, Josef Reichholf, who is biologist talks about role of steppes (grass fields) in evolution of grass eaters, like horses are. It turns out that 1km^2 of grass can sustain 30 tons of mammals, when 1km^2 of forest can sustain only 300kg of animals. That's 100 times less. Even, if the forests were not dense, there still is nothing to eat for the horses.

As if it was not enough, lately it's been discovered by scientists, that at the time of first invasion there was significant climate change, when temperatures dropped almost one degree for several years making pastures less productive and making nomadic army, totally dependent on them, in even more difficult spot. This is minor however in comparison to the economy presented above.

And the last accord is forest itself in warfare. It renders cavalry and archery useless no matter how sparse it is. It was one of the reasons why Charles Martel took battle of Tours in the forest against superior muslim forces. It disabled cavalry for a great part and Moores had to fight "on European" terms, which meant, no speed, no mobility leaving light army forced to fight against armoured troops.

The more to the north, the less settlements, less fields and more forests, making the sustainability of the Mongol army problematic and conquest questionable.