Why are aircraft tyres not grooved horizontally like vehicle tyres? If the tyres are grooved horizontally won't it help in achieving more friction and reduce the chances of veering off?
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.
It's certainly not universally true that all aircraft have length wise grooved tyres only.
Especially aircraft designed for use from rough and unprepared strips often have heavy duty tyres to deal with such conditions.
Think some military aircraft especially. Here's an example of a Sea Fury deployed in Korea during the war there for example:
Linked from www.3rdattackgroup.com
Another example is the He-111:
Picture source. The link points to the full picture.
You have two questions here, lets just consider this for GA/commercial planes that are operated mainly from paved strips. Back country flying and grass/dirt strips lend to other tire needs.
Why are aircraft tyres not grooved horizontally like vehicle tyres?
Short answer, contrary to popular belief groves actually reduce grip. Vehicle tires are also designed to fit a different use case. Summer tires (mainly for dry times) can actually be close to aircraft tires in their cut (full slicks are not legal everywhere). All seasons are made to work well in not only rain but snow and ice as well. As such the groves are cut to displace water as well as provide limited traction on packed snow.
If the tyres are grooved horizontally won't it help in achieving more friction and reduce the chances of veering off?
No, but lets dig in. There are two cases to consider here, a wet runway and a dry runway. The coefficient of friction of rubber on dry asphalt is extremely high ~=.9 but when it comes to using tires to stop something (breaking really) you want the most rubber/asphalt contact you can get (also known as the contact patch). Thus the "grippiest" tire so to speak is whats commonly known as a racing slick since there are no groves. By adding tread you actually reduce grip by reducing the contact patch when talking about a dry runway.
Since airplanes sometimes operate in the wet (let's ignore snow), we need to account for that. To make a tire work well in the wet we need to displace the water so that the rubber can make contact with the asphalt. If you get a layer of water (even a thin film) between the tire and the asphalt you have what is commonly known as hydro planing (no, a seaplane rating won't check you out for this); you can read a full study on it here. Since you only need to provide area to displace the water to the simple groves provide enough space without adversely affecting grip as a traditinal car tread would.
Another somewhat related reason they may not be grooved laterally is to prevent the tires from spinning up which could cause other issues.
Older F1 Rain tires area actually cut very similar to aircraft tires as can be seen here
Compare to this
Runways have horizontal grooves on them to allow more surface area for water/slush to "hide" in. This feature helps keep the thickness of the fluid film low.
Most airplane tires avoid using horizontal geometric features—both blocks and sipes—so that the rubber on these wheels that land at around 250 km/h do not chunk out. At these high pressures the canals or ribs are enough to take care of hydroplaning. Horizontal ends further pose the disadvantage of groove wander if the pitches on the tires match that of the runway.
Moreover, airplane landing gears are designed strategically so that in the H configuration the front tires clear the track of slush for the rear pair to grip in.
Smaller aircraft and "off road" versions—typically small and light weight—have patterned tires. Some use these on the front alone while the rear tires that touch down first are simple rib tires.
Why are aircraft tires not grooved horizontally?
Because, unlike cars where the thrust is a force that acts on the drive wheels, in the point where they touch the ground, and has a forward orientation, the plane is pulled by propellers or pushed by jet engines and the wheels provide no thrust. So, horizontal grooves will not increase the thrust in the case of an aircraft. Even for trucks, the non drive wheels tend to have mainly vertical grooves with some minor horizontal cuts (see the picture).
Regarding "reducing the chances of veering off" the best grooves are the vertical ones because they can catch soil and increase the friction in case the plane tends to veer off course while trying to land. Horizontal grooves will have exactly the worst orientation, to the left and right, acting like skates for that direction.
Recently I came across a Wired article which mentions:
In the first moments after a plane touches down, the tires are skidding, not > rolling. The airplane essentially drags them down the runway until their rotational velocity matches the velocity of the plane. That's why they smoke upon landing, and why Michelin uses grooves instead of the block patterns seen on your car's rubber—blocks would simply break off. (Most tire wear comes from this moment of contact—where the rubber meets the runway.) The stoutest tires are rated for speeds of up to 288 mph.