I have weaned cold turkey before. The others are right in that it often is not as bad as it sounds as long as the foal is old enough. With that said, I will tell you that I have learned over the years that gradual weaning is easier on both the mare and the foal as the mare does get some releif for her bag, and the foal gets the reassurance that it needs as well.
By weaning the foal(s) with a "babysitter" that the foal has know all of it's life, the foal does better mentally IMO. What I have noticed is that some foals that are weaned at 3 months old were full of self confidence and were quiet bold. Then when suddenly weaned, the foal lost all of it's confidence in how life is. Some foals can take several years to really get that back. I have found that gradually weaning a foal doesn't seem to do that to them.
I have to think how nature would wean those foals if they are in the wild. (I know.... minis are "man made", but still, they are equines like the rest) In the wild, the mare will not let the foal nurse after a certain age. Then the foal is still allowed to remain in the herd, but the others keep it in it's place. When the foal is old enought to reproduce, it is at that time that it tends to get driven off by the stallion. But by that time, the foals are several years old. So what I try to do is keep the herd somewhat stable when the horses are at the youngest ages so that they continue to have that family support. That is why I prefer to remove the mare, or at the least take a herd buddy or two with the foal if I have to remove the foal.
Just my thoughts and what I have found works best for me with large breeds as well as miniatures.