Does horizontal motion decrease with the increase in gravity?

If a ball moves horizontally with a constant velocity in Earth compared to a ball moving with the same velocity but in a thicker gravitational field, will the ball move slower in the other plane compared to Earth or will it be the same?

If it moves with the same velocity then it will not be either slower or faster, it is by definition the same.

Although to an observer on each planet it would travel at the same speed, as with everything in physics, it's all relative. To an outside observer, time on the larger planet runs slower than time on earth. So if the ball was thrown across a distance of 100 meters, then the ball on earth would cross the distance before the ball on the larger planet - to the outside observer. Because the denominator of the fraction distance/time is longer, although they are both one second.