Can a weather balloon move horizontally?
An ordinary weather balloon cannot maneuver horizontally (unless an external force is applied to it) because it lacks the means to do that. It has only one purpose, to soar up to the altitude where the air pressure inside is more than outside and then burst.

If you want it to steer, you can add steering servos (as mentioned in this PDF). Of course this will add cost and complexity.

There are some websites for Balloon Trajectory Forecast, which might be helpful.

Only if Larry Walters had thought about this, things would have been different for him.