Aims: We pose the question of how much information on the atmospheric parameters of late-type stars can be retrieved purely from color information using standard photometric systems. Methods: We carried out numerical experiments using stellar fluxes from model atmospheres, injecting random noise before analyzing them. We examined the presence of degeneracies among atmospheric parameters, and evaluated how well the parameters are extracted depending on the number and wavelength span of the photometric filters available, from the UV GALEX to the mid-IR WISE passbands. We also considered spectrophotometry from the Gaia mission. Results: We find that stellar effective temperatures can be determined accurately (σ 0.01 dex or about 150 K) when reddening is negligible or known, based merely on optical photometry, and the accuracy can be improved twofold by including IR data. On the other hand, stellar metallicities and surface gravities are fairly unconstrained from optical or IR photometry: 1 dex for both parameters at low metallicity, and 0.5 dex for [Fe/H] and 1 dex for log g at high metallicity. However, our ability to retrieve these parameters can improve significantly by adding UV photometry. When reddening is considered a free parameter, assuming it can be modeled perfectly, our experiments suggest that it can be disentangled from the rest of the parameters. Conclusions: This theoretical study indicates that combining broad-band photometry from the UV to the mid-IR allows atmospheric parameters and interstellar extinction to be determined with fair accuracy, and that the results are moderately robust to the presence of systematic imperfections in our models of stellar spectral energy distributions (SEDs). The use of UV passbands helps substantially to derive metallicities (down to [Fe/H] -3) and surface gravities, as well as to break the degeneracy between effective temperature and reddening. The Gaia BP/RP data can disentangle all the parameters, provided the stellar SEDs are modeled reasonably well.