Exactly.
Fish was also conveyed in that unique Irish wagon, the "soft-top"; the convertible van with an open centre section on the roof, which was left open for cattle traffic, and covered with tarpaulins for other traffic. These were wain stock, unlike (as Mayner says) horse boxes, and dedicated meat and fish vans.
As for livery, it's not certain that all were in passenger livery on all lines, but as above, most were. Usually this was the base colour but without lining. Rarely was a crest added, though the GSR certainly applied it to to some vehicles. The last incarnation of a wagon in passenger livery would have been the NCC / UTA "Brown Vans", which despite initial fitted WAGON brown in NCC times, then got UTA green, and finally NIR plan maroon.
Even on the narrow gauge, while I'd need to look this up, there was a horsebox or van of some sort on either the West Clare or T & D which the GSR painted maroon, and CIE painted the six wheeled brake vans on the West Clare in green, though a brake van made from a T &.D passenger coach was painted grey.
There were exceptions. While the GSWR used their extremely dark claret, and the GSR their own maroon, and the GNR used mahogany on bread vans, it seems the GNR used wagon grey on other such vehicles.
I am unaware of information on horse box liveries on the DSER and in West Cork, but there is some evidence that the MGWR used GREEN - not unlike their loco green - on horse boxes. The WLWR had a unique livery for them, though I don't know what I think was at this stage.......
Unlike normal-liveried non-passenger stock, when horse boxes and the like received a passenger livery, the chassis was black, same as carriages.