Why are aircraft tyres not grooved horizontally?
Almost all the aircraft operating from prepared surfaces have circumferential grooves in order to remove water between the tyre and runway surface.
From Dunlop site:

Most Dunlop aircraft tyre designs feature circumferential grooves moulded into the tread to disperse water from beneath the tread in wet runway conditions.
The tread helps to reduce the risk of aqua planing and improves traction and grip between the tread and runway surface.

In 1960s, NASA carried out a number of studies to determine the effect of tread design (among other things) for operating on wet runways and settled on the circumferential groove shape.
In case of aircraft operated from unpaved surfaces, the tyres may have some type of cross-tread pattern.