Can alcohol abuse cause horizontal nystagmus somehow?

Yes, alcohol abuse can cause horizontal gaze nystagmus (HGN).

Horizontal gaze nystagmus is an eye movement characterized by involuntary, rapid, horizontal oscillations of the eyes. Nystagmus is classified as either pendular or jerk. Pendular nystagmus is characterized by eye oscillations of equal speed as they move in each direction, whereas jerk nystagmus is characterized by rapid drifts in one direction followed by a slower movement in the opposite direction. HGN is a common finding in acute alcohol intoxication and withdrawal.

Alcohol suppresses the central inhibitory effect of the nucleus vestibularis lateralis on medial longitudinal fascicle (MLF). The MLF connects various brain regions involved in eye movement, including the vestibular system, the oculomotor nucleus, and the abducens nucleus. Loss of the inhibitory influence of the vestibular nuclei results in increased activity in the MLF, which manifests as HGN.