Weather permitting, and assuming the foal is fine with no issues, I get them out the first day after it has cooled down a little, for a short period of time. After that, it all depends on how the foal and mare do. If they are relaxed and not running all over, they get to stay out longer. If the foal is overdoing it, they don’t stay out as long. Eventually I get them out 24/7 during the summer, but I do bring them in at night for the first month or two, so the foals get lots of handling. I don’t leave halters on mares or foals.
I’m a one-woman operation. (Imagine how I must looking administering an enigma to an unwilling foal by myself!)
I let the foals follow the mares for the first couple of days, but by the end of the first week they are leadind outside separately. (Mare goes out first, then foal; foal comes in first, then mare.) I use the butt-rope method. They learn pretty quickly with that, plus, it seems the safest for them and easiest for the handler. I learned not to let them follow behind any longer than necessary a couple of years ago, when a foal following the mare took a u-turn, ran up a manure pile (which now has a removable wall/gate to prevent another incident), and kept going, sailing over the five-foot fence into the round pen. He was fine, but I thought I would have a heart attack, imagining that he had broken a leg or something. (He was sold in-utero.) He was fine, and I do have to say that the look on his face was hilarious.
Of course, there are several ways to do things, and much of it depends on the comfort level of the mare and foal, and sometimes that of the handler! 
Let us know how everything goes, and good luck with her foaling!