I hate breakaways on foals. If you're just wearing it in the field... ok fine. BUT when theyre young they arent going to leave thier mother so there really isnt reason to leave a halter on them turned out at all. And by the time that they do leave their mother, you should be able to halter them at any point anywhere and lead them.
Breakaways cause too much trouble when learning to tie and lead and such. If it breaks once when they throw a tantrum, guess what, they just learned how to get out of doing something they don't want to do. You may not think they break that easy, but they really do. It makes breaking a young horse a nightmare. I wont use them.
As for nylon or leather, it doesnt really matter. Me personally, I use nylon because its cheaper and you go through a few halters with foals because they grow so fast.