While your inclination might be to coddle and protect your mare's new foal, it's really not good for him.
Several recent studies have shown that foals raised on 24/7 turnout have significantly stronger bones, joints and ligaments than stall-raised foals or foals that spend part of the day confined in stalls. In fact, the ones confined part of the day, then turned out were more likely to injure themselves letting loose that pent-up energy. Raising foals outdoors also reduces the chances of respiratory infections or allergies developing.
The ideal setup is a generous-size field, preferably at least two acres, for the foal to play, graze and roam in, with access to a roomy run-in shed as needed to avoid the sun, bad weather and bugs.