Two lines are parallel if they do not intersect at any point.
Another way of thinking on parallel lines is: two lines are parallel if they have the same slope.
On the other hand, all horizontal lines have the same slope, which is equal to 0.
Since all horizontal lines have a slope equal to 0, this means that all horizontal lines are parallel.
Therefore, the answer is: yes. All horizontal lines are parallel.
Notice: This is only valid in 2D.