One of the mechanisms thru which steroids work, is that they cause a massive increase in IGF-1.
IGF-1 rapidly increases the division rate of cells, including muscles cells, hence the ability to grow and repair at a much accelerated rate, leading to big gains in muscles.
Of course the downside of this rapidly increasing rate of division is that you are effectively aging yourself faster. Over time as cells divide you introduce more "mistakes" in the DNA as each cell divides. These cumulative mistakes are what contributes to aging as you move from a collection of health cells to unhealthy cells.
Obviously there are other factors at play from a cosmetic perspective, constant sunbed use to maintain color, someone of African descent will not look as bad as someone of European descent as their skin can come with UV damage more effectively.
The dosages used, diet, genes, general lifestyle, these all play a part but fundamentally there is no getting around the fact at the base level steroids age you faster.