RAW explicitly empowers the DM regarding hiding
The rules for hiding explicitly mention that the DM decides when hiding is appropriate, and that you may give yourself away if you make noise. (This empowerment is on top of the general authority the DM is given on rules, as it is explicitly called out in the Hiding rules.)
The DM decides when circumstances are appropriate for hiding. [...] You can't hide from a creature that can
see you clearly, and you give away your position if you make noise,
such as shouting a warning or knocking over a vase. (Emphasis mine.)
It is very reasonable for the DM to have decided that the "stony environment" you were in would cause you to unintentionally make noise if you were to have moved at your full speed.
Ideally, if that were the case, the DM would explicitly say that was the reason for the half speed movement. If they didn't, I would suggest asking them for the reasoning behind that to clarify future expectations. (They may also have been confused regarding the travel pace rules, or older editions, which other answers discuss.)
That said, no, there is no rule that requires half speed, or causes any other negative effect on a character that is hiding.
I added this answer in large part because I felt an existing answer at the time implied that the DM was wrong to make the ruling they did, and wanted future visitors to this question to understand the leeway the DM has in deciding what is appropriate for a hiding character.