Unlike vertical drills where the drill bit is weighted down by gravity, in horizontal drilling, the drill string is pushed into the rocks. How does the drill pipes not snap under the immense force, especially since the pipes can end up being curved?
It's called engineering design. The drill steels are designed to withstand the forces required of them. This incorporates materials used, manufacturing techniques, the design of couplings, rigidity/flexibility of the drill steels & drilling method: rotary, percussion or a combination of the two, rotary-percussion.
Long holes drilled in rock, whether vertical or horizontal, are usually drilled by rotary drill rigs. Depending of the reason for drilling a hole, the type of drill bit used for such holes will be either a diamond drill bit or something like a tri-cone bit.
The diamond drill bit is used when rock samples need to be recovered. Tri-cone bits, or similar, are used when a hole need to be established for other reasons, such as an oil well.
With rotary drilling, the drill steel experiences torsional forces from the drill head and only needs sufficient compression force to keep the drill bit engaged with the rock face at the end of the hole. If there is too much compression the drill steel with bow which can lead to rubbing against the side of the hole and excessive wear of the drill string. With too little compression there will not be enough contact with the rock face and the advance rate will be low.
If drill strings do not have a good method for removal of the drill chips the drill bit and string will jam in the hole. This is why percussion and rotary-percussion drilling is not used to drill long holes, particularly horizontal holes or vertical down holes.
The drill is not really pushed in the horizontal section. The drill pipe is not very unique, mostly high strength steel like 105 Ksi yield strength. The magic is the other equipment. Mud motors turn the drill bit , the drill string itself may not even rotate ( that reduces the fatigue loads) and the "measure while drilling" technology that tells where the bit is and where it is going. When I retired from an oil company , turbines were sometime used the turn the bit, apparently now it is all mud motors ( look it up in Wiki, etc.).The energy to cut the rock is supplied by the very high pressure mud pumped through the pipe. ... I was on the API committee that wrote the specs for drill pipe ; we pretty much wrote what the drillers wanted. The oil company hires a drilling contractor and he rents the drill pipe from a third party , so oil company metallurgists like me, seldom sees drill pipe problems. Drill pipe never has couplings , it has "rotary shouldered connections", also called integral joints. A larger diameter section with internal threads ( box) is welded to the drill pipe , male threads (pin) are cut at the other end. Often the string is "hard banded" where tungsten carbide is welded in bands to protect the string from wear against the steel well casing and the formation. Not a panacea as it may cut through the steel casing. The oil company must calculate the strength and size of the casing for each section of the well . The driller must calculate the curvature to be within limits for the particular drill pipe; Of coarse the driller and oil company need to work together; It would be embarrassing to find the drillers rig was not able to lift the required casing string. This is a brief over-view of about 10 semesters hours of petroleum engineering school .