Video proof that the Donner-Reed Party Blizzard is delibrately programmed into the game, and, given the right circumstances, will happen to your party. The length of time you spend varies, as seen in the video I wasn't even trapped for a month, but it guaranteed to happen.
To make this occur to you, set the date at the beginning of the game to April 1846, start at Independence, and head for the Sacremento River Valley as an adventurer or trail guide. At the Sublette Cutoff, take the road to Fort Bridger, then head for the Salt Lake Alternate Route, and finally the Hastings Cutoff. This is the same route that the Donner-Reed Party took on their journey. If there have been no large delays in your journey, you should reach the Sierra Nevadas by the end of October, where the blizzard is waiting for you.
Incase you are unfamiliar with the Donner-Reed Party, here is an excerpt from Wikipedia:
"The Donner Party (sometimes called the Donner--Reed Party) was a group of American pioneers who set out for California in a wagon train. Delayed by a series of mishaps, they spent the winter of 1846--47 snowbound in the Sierra Nevada. Some of the emigrants resorted to cannibalism to survive, eating those who had succumbed to starvation and sickness.
The journey west usually took between four and six months, but the Donner Party was slowed by following a new route called the Hastings Cutoff, which crossed Utah's Wasatch Mountains and Great Salt Lake Desert. The rugged terrain and difficulties later encountered while traveling along the Humboldt River, in present-day Nevada, resulted in the loss of many cattle and wagons and contributed to divisions within the group.
By the beginning of November 1846 the group had reached the Sierra Nevada where they became trapped by an early, heavy snowfall near Truckee (now Donner) Lake, high in the mountains. Their food supplies ran low, and in mid-December some of the group set out on foot to obtain help. Rescuers from Sacramento, California, attempted to reach the emigrants, but the first relief party did not arrive until the middle of February 1847, almost four months after the wagon train became trapped. Forty-eight of the 87 members of the party survived to reach Sacramento.
Historians have described the episode as one of the most spectacular tragedies in Californian history and in the record of western migration."