It is mostly guild-based. However, there are options for casual RP.
There’s a casual gathering every Sunday at a different location. These usually attract a decent number of attendees.
There are Fireside Gatherings on the first Saturday of every month, where guilds are encouraged to gather in Orgrimmar to participate in various events. They are usually quite successful.
You’ve also got seasonal public events like the Conquest Clash tournament and the Kosh’harg Festival. Spring is coming, so I would expect the next Kosh’harg in the next couple of months. These tend to be absolutely massive.
But if you are looking for a solely Horde roleplaying hub where you can find people casually roleplaying every night, there isn’t one. People don’t bother with Orgrimmar these days unless their guild is passing through and it’s a similar story for Silvermoon City.
If you’re open to cross-faction RP, then Legion Dalaran is your best bet, though it is decidedly neutral and so it may not suit characters who care a lot about the Horde and who are built around the Horde’s themes.