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In galaxy clusters, the hot intracluster medium (ICM) can develop a striking multiphase structure around the brightest cluster galaxy. Much work has been done on understanding the origin of this central nebula, but less work has studied its eventual fate after the originally filamentary structure is broken into individual cold clumps. In this paper, we perform a suite of 30 (magneto)hydrodynamical simulations of kpc-scale cold clouds with typical parameters as found by galaxy cluster simulations, to understand whether clouds are mixed back into the hot ICM or can persist. We investigate the effects of radiative cooling, small-scale heating, magnetic fields, and (anisotropic) thermal conduction on the long-term evolution of clouds. We find that filament fragments cool on time-scales shorter than the crushing time-scale, fall out of pressure equilibrium with the hot medium, and shatter, forming smaller clumplets. These act as nucleation sites for further condensation, and mixing via Kelvin–Helmholtz instability, causing cold gas mass to double within 75 Myr. Cloud growth depends on density, as well as on local heating processes, which determine whether clouds undergo ablation- or shattering-driven evolution. Magnetic fields slow down but do not prevent cloud growth, with the evolution of both cold and warm phase sensitive to the field topology. Counterintuitively, anisotropic thermal conduction increases the cold gas growth rate compared to non-conductive clouds, leading to larger amounts of warm phase as well. We conclude that dense clumps on scales of 500 pc or more cannot be ignored when studying the long-term cooling flow evolution of galaxy clusters. [ABSTRACT FROM AUTHOR]