Tyre size, construction and weights need to be considered along with what psi you normally load them with in the first place but dropping by half wouldnt be a good idea at all., at 25psi my vans would run off the rim and the Jeep at 30 would end up with the sidewalls ripped out........... My van runs at 47 and the Jeep at 45 rear on the sealed road (towing), so if let down for dirt I'd drop probably 4 psi cold, depending on the road surface ..... The differences in tyres is huge so the psi you use is your choice, never use what someone else advises unless you know the tyre type in question............ My tyres are LT265 75R16, ATR's they have a max pressure of 80 psi while others are smaller and have max pressure of maybe 45 psi, so it pays to know what your tyre is capable of and never run at max psi.....
Vans should have LT tyres then you have a greater variation in psi and the tyre placard is a guide for the original tyre once you change tyres the placard becomes irrelevant and correct pressure on sealed roads is always 4-6 psi above the cold pressure no matter what is said in a book or label...... so on dirt 4-6 psi below cold is a rule of thumb with a drop in speed, as it gets rougher then I get slower , I hate opening the tool box.....
The thing is, what has been loosened on the dirt may not show up until miles later when you are banging down the highway, so a proper check when parked up of the rig is essential, boots and a rubber hammer seem to do the job, sounds over the top but I rarely have to stop and fix things..