Except, that is, on the first Sunday of each month. Then the cobbled square hosts a horse fair where throngs of youngsters swarm over ponies of every age, size, shape and condition.
Some test-ride them bareback along side-streets that resound to the clatter of galloping hooves on stone. Fists of notes change hands and new owners, some dwarfed by their new pets, lead them to the spartan grey estates of Ronanstown, Neilstown, Clondalkin and Tallaght to the south- west, and Finglas, Ballymun and Darndale on the northside.
Here the animals graze on public land, or are accommodated in makeshift breeze-block stables in backyards. Ballyfermot has one particularly down-at-heel network of Corporation terraces where cars are seldom seen, but every other front lawn has a piebald pony.
Images of exuberant "chisellers" (kids) astride large horses in films such as Into the West and the Roddy Doyle drama The Commitments might seem surreal. But Doyle has staunchly defended his depiction of horses being led into multi-storey tower lifts, or ridden off the Dart, the city's suburban electric train service
Most Dubliners in these suburbs have their own equine tales of the unexpected. A primary school teacher recently asked a 10-year-old why he was covered in wet mud at 9.30 on a Monday morning. "I fell off me horse, miss," he replied. At another northside school, pupils were known to arrive on their own 1 hp transport, left tethered to school railings chewing grass verges until lunchtime.
The sight of horses grazing among the treeless concreted sprawls of Dublin's satellite towns highlights the anomaly.Rural Ireland was synonymous with equine breeding long before vast fairs such as Ballinasloe supplied British cavalry regiments with horses in their thousands. But by the Seventies, this was only a folk memory in a city where the stables of Georgian townhouses had been developed into up-market bijou homes. The closest contact most Dubliners had with the animal was in the betting shop.
But concern over strays, ill-treatment of horses and young bareback riders running riot has made controlling urban horses a political issue. Up to 50 are sometimes to be found grazing on unfenced open spaces. Last year, local authority workers impounded 296 ponies in Tallaght and 294 from Clondalkin, at a cost to taxpayers of IR£70,000. Last September, moves were made by the city corporation to close the Smithfield market. After protests it relented, giving traders six months to co-operate with the Dublin Society for the Prevention of Cruelty to Animals (DSPCA), gardai and vets on improving standards. Recent serious accidents involving untethered ponies have sharpened residents' concern and led to a Bill being drafted to regulate the sale of urban horses.
Last month, two-year-old Stephen Domican suffered serious head injuries, and risks losing an eye, after being kicked by a stray horse while playing outside his home in Clondalkin. Earlier this month, in Tallaght, four- year-old Samantha Kennedy was kicked in the face by a loose animal.
Travellers, or Irish gypsies, are widely credited with re-introducing the horse to Dublin. By the Seventies, a number of travellers were exchanging their nomadic life for public housing. Gradually they began to exploit their traditional contact with breeders of less expensive ponies as a new urban business. Travellers were among those supplying the new Smithfield market in 1978. The prestige that went with owning a horse and the lack of recreational alternatives in ill-planned estates helped to make a horse the adolescent status symbol of the Eighties.
Therese Cunningham of the DSPCA estimates the city's horse population to be several thousand. The hazard of ponies wandering into the paths of unsuspecting motorists fuels pressure for legal controls. Motorists involved in these collisions also risk financial disaster. If a stray animal's ownership cannot be traced, a driver may find insurance compensation impossible to obtain.
This happened to Mairead Fitzgerald, whose new car was destroyed in 1991. "The horse literally jumped on to the bonnet of the car and came through the windscreen," she told the Irish Times.
The fall of the Albert Reynolds government last November has indirectly led to increased pressure for controls. The new "rainbow" coalition included for the first time Democratic Left (DL), whose two Cabinet members, Proinsias de Rossa and Pat Rabbitte, represent the depressed areas of north and south-west Dublin where loose ponies are a public safety issue. Among other demands, they have insisted that control of horses become coalition policy.
The new Bill is expected to require licensing and registration of all horses, and will probably include provision for branding, a ban on sales to minors, and charges for the release of impounded strays. A horse would be automatically sold when impounded for a third time.
Ms Cunningham hopes this may help to clean up the trade in cheap, old, sick and injured horses. Last week in the DSPCA stables at Rathfarnham, just below the Dublin mountains, were two prime cases, a pair of Shire horses brought to Smithfield from England by an Irish dealer. Aged 10 and 15 years, the once-powerful 19-hand working horses were given to the DSPCA in return for no charges being brought against the trader. "They were in an appalling state - emaciated, covered in mud-rash, with hardly any hair, infested with lice, and with their faces badly scarred from scratching against walls," Ms Cunningham says.
A pioneering project in one inner-city suburb shows how the authorities might apply a more positive approach to Smithfield's customers. In Finglas South in the late Eighties, a local youth project perceived in the horse craze a way to reach out to young people whose employment prospects were minimal. Hilary Tierney, an experienced horsewoman, began helping the youngsters to obtain cut-price fodder and a subsidised weekly vet's visit.
The scheme ran successfully for four years. Children would gather round the vet, learning for the first time basic grooming and horse husbandry. Animal health improved, youngsters learnt to buy better, fully grown horses, more suitable for riding. Older boys passed on their knowledge to youngsters. Some built proper stables and arranged their own blacksmith. Financial help came from international horse charities.
The problem of local strays was also eased, says Adrienne Ward of the Rivermount Project. "Companies like CRH Roadstone [suppliers of road- building materials] had a lot of strays on their property, which was a problem for them with [accident] liability." The solution was found in making young urban cowboys into nominal ranchers of the inner-city range: grazing leases were provided at a minimum IR£2 a year, protecting the corporate owners against damages.
A local secondary teacher believes that horse-owning can be a good thing, occupying boys who might otherwise lapse into petty crime, joyriding, or another highly dangerous Dublin craze, "company cars". This involves racing dangerous old bangers, bought with pooled pocket money by groups of youths for about IR£50, exploiting the (soon to be closed) loophole left by Ireland's lack of compulsory MoT-type tests.
"They can seem like bleeding savages sometimes, but they really care for them," he says. "It's a status symbol, especially if they've got a good horse. It's one of the few things that really interests them."