5 of my 8 babies were born outdoors or in a clean stall with the indoor/outdoor option. Weather pending they were left to their indoor/outdoor option and the three stall born babies were turned out with-in a day or two of being born weather pending.
I have always kept mommas & their foals separate until things settle down with the other horses, usually 10-14 days then a let them join a friend, other mares or the herd depending on my living situation and horse arrangement at the time. Your mare, foal and your herd will dictate how long you wait and when you feel that it is safe.
Our little orphan Hijinx was born outside, when his dam passed away I tried to keep him separate with just the goats and one buddy but no one was having any of it. At just five days old he was in our herd of 14 horses with no momma, but the four that kind of took him under their wing helped him out and everyone seemed to watch out for him and keep him safe.