Momentum question, mass and velocity?

Alright, here's my question. If you have a train moving at a constant velocity that's attached to an empty freight car with no top and it is raining. Will the train start to slow down because the mass is increasing? or will it keep it's constant velocity (pretend that it is raining so hard that the freight car could be filled within minutes). Also if the case is that the train slows down because of increase in mass does that mean mass is inversely proportional to velocity? Please answer, thank you!