Greater Manchester is dense and largely built-up, but it sits with genuinely good grazing country on three sides — the Pennine fringe to the east, and Cheshire and Lancashire close by to the south and north — so families rarely need to compromise for long. Riding schools within the conurbation itself are plentiful, serving a huge population who want lessons and pony experience without owning land themselves.
Motorway links are a real advantage here: the M60 and its connecting motorways make it straightforward to view ponies across Cheshire, Lancashire and the Peak District fringe in a single day, effectively giving a Manchester-based family a much wider practical search area than the county boundary suggests. Expect city-adjacent prices for anything kept close to the conurbation, and better value the further out toward the moors you look.