Hertfordshire is solidly London commuter-belt country, with green-belt land protecting a surprising amount of countryside close to the capital, but that same protection means grazing is limited and fiercely sought after. It has an active Pony Club and riding scene serving a well-off, riding-literate population, and good road links make it easy to widen a search into Essex, Bedfordshire or Buckinghamshire.
Expect to pay for what you get — grazing near the M25 corridor and around St Albans carries a real premium, and many ponies here are on livery yards rather than private fields. If budget matters more than proximity to London, the north of the county toward Bedfordshire and the Hertford/Ware area tends to offer better value than the areas closer to the capital, without losing the county's generally good facilities and knowledgeable local horse community.