lol... its not beside the point and something which had to be taken into account. If there wasn't any slowing down, things could get ugly trying to disembark, eh?
If you really meant, 'whilst travelling at", you could be quite right about the headlights, but the ball travelling "It travels at the same speed as it does when thrown when the carrige is stationary." still applies in motion at any speed, depending on the observer's viewport
Observed on the carriage, the ball would possibly be as you suggest, but, observed from outside (as a passerby) you get something different.
Dayglow's cartoon (frames 5, 6 and 7) explains "observer" and "viewport" rather well