Context. The coldest metal-poor population made up of T and Y dwarfs can serve as an archaeological tracer of our Galaxy because these very old objects have retained their pristine material. The optical properties of these objects are important for characterising their atmospheric properties. Aims. We aim to further characterise the optical properties of the ultracool metal-poor population with deep far-red optical images and parallax determinations. Methods. We collected deep optical imaging of 12 metal-poor T dwarf candidates and the only potential metal-poor Y dwarf (known as the 'Accident') using the 10.4-m Gran Telescopio Canarias, the 8.2-m European Southern Observatory Very Large Telescope, and the Dark Energy Survey. To infer their distances, we have been monitoring the positions of five metal-poor T dwarf candidates for two years, using the Calar-Alto 3.5-m telescope. We compared these objects with a known subdwarf benchmark and solar-metallicity dwarfs based on colour-magnitude and colour-colour diagrams, as well as with state-of-the-art theoretical ultracool models. Results. We solved for the trigonometric parallaxes of the five metal-poor T dwarf candidates. We obtained z'-band photometry for the other 12 metal-poor T dwarf candidates, increasing the sample of T subdwarfs with optical photometry from 12 to 24. We report a 3-σ limit for the Accident in five optical bands. We confirmed three more T subdwarfs and found that the Accident is sub-luminous compared to the current Y dwarf limit. In addition, we have proposed two more Y subdwarf candidates. We emphasise that the zPS1‑W1 colour combined with the W1‑W2 colour could break the metallicity-temperature degeneracy for T and could possibly break it for Y dwarfs as well. The zPS1‑W1 colour shifts redwards when metallicity decreases for a certain temperature, which is not predicted in current models. The Accident has the reddest zPS1‑W1 colour among our sample. The zPS1‑W1 colour will be useful in searching for other examples of this cold and old population in current and upcoming deep optical and infrared large-area surveys.