The answer to this question depends entirely on your approach to film. Do you see it as part of the historical record, as a creative medium, or as a product to be marketed?
If you approach film as a historian would, as a primary source evocative of its era, then colorizing film would be absolutely wrong. In that case, to colorize the film would be to falsify it as a historical record. Colorizing would mislead uninformed viewers and would take away from the film's authenticity as a vehicle for conveying historical information. If the original filmmakers did not create the film in color, then it should remain in black and white.
If you approach film from an artistic standpoint, however, colorizing film could be a creative endeavor, adding a new dimension to the original black-and-white images. And if you approach film from a business perspective, perhaps adding color would bring in new audiences who may be put off by the starkness of a black-and-white film.
My own personal opinion? I approach film from a historian's standpoint, so I prefer that films remain in their original condition, to help me understand more clearly the era in which they were made. Film speaks to people in many different ways, however, so I realize that others may not approach film in quite the same way that I do.