It first appears in the mission Election Campaign, where you must use this gun to assassinate a politician. It is later used by the Port of Lost Heaven guards. Finally, in Free Ride Extreme, you use it in Sniper Mission.
This is the only rifle in the game that features scope view; however, it is more difficult to aim accurately at a great distance due to the scope view slowly swinging up and down with minor random deflections to the left and right.
You can find more real world information about the Mosin-Nagant 1891/30 on its Wikipedia page.