Magnetic-field-induced ordering of electrons around vortices is a striking phenomenon recently found in high-T(c) cuprates. To identify its consequence in the quasiparticle dynamics, the magnetic-field (H) dependence of the low-temperature thermal conductivity kappa of La(2-x)SrxCuO4 crystals is studied for a wide doping range. It is found that the behavior of kappa(H) in the subkelvin region changes drastically across optimum doping, and the data for underdoped samples are indicative of unusual magnetic-field-induced localization of quasiparticles; this localization phenomenon is probably responsible for the unusual "insulating normal state" under high magnetic fields.