These rules are for England.
What you need depends on one split: livery means keeping horses that belong to other people, and riding services means providing horses for other people to ride. Livery alone needs no licence. Riding services do.
Hiring out horses needs a licence
You do not need a licence for livery alone, for grazing, for teaching people on their own horses, or if your trading income from hiring out horses is below the trading income allowance.
Check planning before you build or convert
Work out the VAT on each service
What you must insure
Legal basis
Primary legislation and key regulations