ModelRailroadForums.com is a free Model Railroad Discussion Forum and photo gallery. We cover all scales and sizes of model railroads. Online since 2002, it's one of the oldest and largest model railroad forums on the web. Whether you're a master model railroader or just getting started, you'll find something of interest here.
Somewhere along the line of looking at RR pictures I've seen some that gave a partial view of the undersides of cars. Mostly I think they were just dusty and slightly rusty. You'll have to position yourself under a bridge (or off to one side) and take a few shots or a movie.
Most train cars are painted the same color on the underside as the rest of the car. However, road grime quickly obliterates most of it ! Below are comparisons of a new Athearn box car I weathered. You can see the weathering pretty much eliminates most all of the original color. Weathering the sides of the car can also greatly reduce that bright color as well ....
Mark pretty much has it correct. Most cars undersides were painted in the basic body color, but there were exceptions. Best way to determine what a car's undersides were painted in, would be by obtaining a copy of a RR's book of standards. The RR's books would generally cover one or two types of items. As such one would cover structure and signs, another would cover rolling stock, etc.
Copies of these books have been published over the years by railroad authors, and historical societies. You just have to make sure the book you're looking through/reading covers the date of the car, whether its the original built date or the repaint date.
