We report on the recent observation of new spectral lines of cold H(3)(+) ions lying well in the visible spectral region. Transitions from the two lowest ro-vibrational levels to final levels up to 16,700 cm(-1), almost half way to the dissociation limit, have been measured, involving up to eight vibrational quanta. The observed transitions are more than six orders of magnitude less intense than the v(2)(1) fundamental band and yet another order of magnitude weaker than reached by previous sensitive action spectroscopy in the near-infrared region. The measurements were carried out in a cryogenic 22-pole ion trap with H(3)(+) ions cooled to their lowest rotational levels by helium buffer gas. Laser-induced chemical reactions lead to the formation of ArH(+) ions detected with single-ion sensitivity. These visible measurements, together with the previous near-infrared measurements, have helped to further develop empirically corrected calculations and have provided essential benchmarks for new ab initio calculations that now reach a spectroscopic accuracy of 0.1 cm(-1) on average up to the highest observed transition. Highly sensitive action spectroscopy and the attained high-accuracy predictions will enable us to find and measure transitions even further into the visible region of H(3)(+), paving the way towards the dissociation limit.