We study the Spectral Energy Distributions, SEDs, (from FUV to MIR bands) of the first sizeable sample of 34 low-luminosity radio galaxies at high redshifts, selected in the COSMOS field. To model the SEDs we use two different template-fitting techniques: i) the Hyperz code that only considers single stellar templates and ii) our own developed technique 2SPD that also includes the contribution from a young stellar population and dust emission. The resulting photometric redshifts range from z ~0.7 to 3 and are in substantial agreement with measurements from earlier work, but significantly more accurate. The SED of most objects is consistent with a dominant contribution from an old stellar population with an age ~1 - 3 10^{9} years. The inferred total stellar mass range is ~10^{10} - 10^{12} M(sun). Dust emission is needed to account for the 24micron emission in 15 objects. Estimates of the dust luminosity yield values in the range L_{dust} ~10^{43.5} -10^{45.5} erg s^{-1}. The global dust temperature, crudely estimated for the sources with a MIR excess, is ~ 300-850 K. A UV excess is often observed with a luminosity in the range ~ 10^{42}-10^{44} erg s^{-1} at 2000 A rest frame. Our results show that the hosts of these high-z low-luminosity radio sources are old massive galaxies, similarly to the local FRIs. However, the UV and MIR excesses indicate the possible significant contribution from star formation and/or nuclear activity in such bands, not seen in low-z FRIs. Our sources display a wide variety of properties: from possible quasars at the highest luminosities, to low-luminosity old galaxies.
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