It is the scholarly consensus that the material after Mark 16:8 is not original to the gospel and was a later interpolation.
There are two endings added to the gospel, the "Shorter Ending" and the "Longer Ending." The Longer Ending consists of the verses you quoted, whereas the Shorter Ending consists only of an additional verse 9, which reads:
They promptly reported all of these instructions to those around Peter. Later, through the work of his disciples, Jesus sent out, from east to west, the sacred and undying proclamation of eternal salvation. Amen.
Neither ending meshes well with the rest of the Gospel. There are theological terms and later Christian ideas that are not found elsewhere in Mark, e.g., "sacred and undying proclamation of eternal salvation." In addition, the Longer Ending shows the influence from other gospels, such as Luke (the Road to Emmaus), John (the appearance to the Eleven in the Upper Room), and Matthew (the Great Commission).
But even more so, these additional endings undermine one of the major theological points of Mark's original.
The Gospel of Mark has a number of key themes: the Messiah as Suffering Servant, the call to discipleship that is willing to take up suffering ("take up your cross and follow me"), and the future expectation of the Kingdom of God.
This last point, a point of eschatology, or theology on the end, is borne out in a number of ways in the gospel but most significantly by the prevalence of the cross. The cross looms exceedingly large in Mark's gospel and points toward the as -yet unredeemed nature of the world. This point is made further by Christ's agony in the garden and his last words, the lament "My God, my God, why have you forsaken me?"
There is a lot of speculation about the composition of Mark's gospel, but most scholars believe it was written in the late 60's of the first century to a mixed Jewish and Gentile Christian community in Rome. During the 60's the Christians of Rome came under the first major persecution by Roman officials under the Emperor Nero. Many of them no doubt wondered why they were suffering if they were worshipping the one true God and following his chosen Messiah. Indeed, much religion in the ancient world was meant to get you out of trouble and bad fortune. Mark's gospel seems to be written to those who are suffering and says, in effect, that suffering is how Christian faith is to be understood. Christ is the Suffering Servant messiah who comes to serve rather than be served, and we, as his disciples, are called to take upon his suffering as our own, rather than seek glory (as the disciples in Mark's gospel so often mistakenly assume).
Thus, the gospel is clear that the world is still in the process of being redeemed and that there is much brokenness still in the world. Having the gospel end on a cliffhanger—with the women fleeing from the empty tomb in fear and not saying anything to anyone—is the perfect illustration of this unfinished work of redemption.
Given all that, it is then strange to say in the very next verse that the women did go and tell the disciples and that the disciples went out into all the world to proclaim salvation. Now, as a historical matter, of course the women told someone and the disciples did go out, otherwise there'd be no Christianity, but the Gospel is trying to make a theological point.
In the same way, throwing in a number of post-resurrection appearances and the ability to handle snakes without death or injury, is substantially different not only in tone, but in this essential piece of Mark's theology: we are still waiting for the final consummation; the tomb is empty but the cross still looms large.
For all these reasons, the Shorter Ending and the Longer Ending are understood to be later interpolations, written by scribes who were uncomfortable with the cliffhanger ending and who preferred some kind of resolution to the story.