By the latter part of the 13th century, the Mongols' frantic territorial expansion was losing momentum. In the east, their empire reached the Pacific, and their efforts to conquer Japan were thwarted by the famous "Divine Wind". In the south, their empire reached both the Himalayas and China's historic southern border. In the west, the expansion of the empire's Middle Eastern fiefdom, the Ilkhanate, was checked at the Battle of Ain Jalut in 1260, while the Golden Horde, the empire's Eastern European component, had its armies annihilated during the Second Mongol Invasion of Hungary in the winter of 1285-86.
But what about the north? Why did the empire not expand all the way to the Arctic Ocean? On one level, the answer is obvious and straightforward: the territories to the north of the Mongol empire were extremely inhospitable and, from the Mongols' point of view, did not contain much in the way of resources worth extracting. But this answer does not explain why the boundaries were set where they were set specifically, and not, say, a hundred miles to the north or to the south.
A Possible Answer
The Mongols, of course, were great horsemen. Their armies employed vast numbers of horses, and the only way practical means of feeding so many horses for more than a single campaign would be to pasture them in massive tracts of grassland. Such grasslands are easy to come by in the southern portions of Siberia, but venture any further north and one runs into the taiga: dense coniferous forest with little vegetation that could sustain a horse. Is it possible that the taiga turned back Genghis Khan and his sons? Comparing the northern boundary of the Mongol empire with a map of Russia's biomes, it does seem that way; although the Mongols' control over the region around Lake Baikal remains to be explained by such a hypothesis.
The various maps of the Mongol empire which I consulted - no two are quite the same, even for the same date - are almost unanimous in stating that at least some portion of the Amur river formed a part of said empire's northern border. This suggests to me that, at some point, the Mongols made a conscious decision not to cross the Amur. But is there any other evidence for that point of view?
Khanate of Sibir
The Khanate of Sibir emerged from the collapse of the Mongol empire, and this state did extend as far north as the Arctic Ocean. (I am basing that claim wholly on the Khanate's Wikipedia page, which itself quotes page 148 of Riasanovsky's History of Russia (1999).) Was this Khanate truly Mongolian in character? That might seem like an unacceptably vague question. What I mean to ask, more specifically, is: was the Khanate of Sibir ruled by a corps of horsemen wielding composite bows? If so, that would seem to refute my hypothesis about the Mongols' advance being halted by dense forest, since the Khanate extended deep into the taiga; if not, then it might confirm it. The accounts of the Battle of Chuvash Cape that I've read seem to imply that the bulk of the Khanate's forces were foot archers, and not cavalry. Is that correct?