I've entered
"Registration for carriages and coaches in Victorian times" in the Google search box. It's offered me
Horses in Victorian Times. It's an interesting article but I can't see any mention of them being registered.
Click here for pictures of a Hansom Cab, a Dog-Cart, a Trap, a Brougham, a Clarence, a Landau, a Wagonette, a Drag, an Omnibus and a Van.
I 've found licences were required for horse drawn vehicles in Vienna in the late seventeenth century and early eighteenth century ... now all that's needed is to see what the situation was in Ireland.
The well researched article in Laura Peel's website titled
Horse-Drawn Cabs,Their Drivers and Their Times refers to licences being required for Hackney Cabs in London in the seventeenth century. Generally what happened in England also happened in Ireland.
Christopher