An engineer’s three cents on why Hordak can read:
1. He works with very complex quantum mechanics/time-space warping physics. He has equations and algorithms on his screens that Entrapta recognizes. He must be utilizing a mathematical language that is commonly used on Etheria, not only in the Horde’s hive mind. It’s possible that the Etherian mathematical notation is a relic from the time before the planet was plunged into Despondos and has has not been altered since (which I doubt), and somehow it was incorporated into the hive mind. Or, Hordak taught himself/was taught the notation on Etheria.
2. As a specialist on robotics, space- and cybernetic technology, he needs to understand both low-level and high-level programming languages, plus databases and interface crafting. It’s possible the hive mind/Etheria has a single language that both addresses logical operations on a chip level and high-level algorithms in all the areas mentioned (at the moment on our mundane Earth you’ll need a large pile of technologies to do such impressive full-stack development). But you need to be able to read and write it.
3. How did he develop his nerve/muscle-enhancing armor that works as a life support? He has ports to access biological functions, but how did he know how to program his armor without the skill to enhance operations possibly on a cellular level? That armor seems like something outside the scope of the hive mind, and he may have added ports on himself besides.
4. Notes and documentation. You don’t program without a proper documentation, unless you know exactly how to read your own code. Which requires reading abilities.
5. He could of course have a voice-operated programming/compiling platform, but did it already exist on his broken ship? If not, did he program one himself? Aaand we’re back to the original argument.
6. Perhaps he just couldn’t read the First One’s language. Which doesn’t make sense, as Entrapta would most likely have conveyed her knowledge of it to him. She cannot read it perfectly, but there’s an episode where she decodes portions of Mara’s signal. It’s also interesting that when he hears of Entrapta’s “betrayal”, his hand flies to the LUVD crystal. If he had no clue as to what was written on it, why was this particular piece of his armor so important? He could have fumbled at any portion of it. So why was this particular detail so dear to him, not to mention that after having been twice mind-wiped, seeing it instantly retrieved memories of Entrapta?
7. Grrrr. Think about it logically.