Once the children are given their independence at snack time Emma you will wonder why you had your current system. There is so much to be gained from letting the children do as much for themselves as possible.
Have a brainstorm with your staff and come up with other things they could be doing rather than getting the children's coats on to go outside which might give your slower eaters a bit more of a chance if you all have snack at the same time - we all had snack at the same time at my setting, but that's not to say we didn't try to change that, we trialled doing snack bar/rolling snack for a whole term we just couldn't get used it it - neither the children nor the adults. What we came up with in the end was a self service system, and jugs on the tables etc. Children helped to make the snack and lay it out for everyone. At the end of snack one or two were helpers collecting up cups and plates etc others "cleaning" the tables (an adult would go around afterwards cleaning, but out of sight of the children) Ours self-registered each morning when they arrived, and so the same name cards were used again to "pay" for snack - as Finleysmaid explained, our youngest were 2 and a half - some jobs were a rite of passage!
Perhaps there's another group nearby you could go and observe? Could your LEA set this up for you, so that you can see it work in action. Sometimes it is hard to believe just how much the younger children are capable of without seeing it for your own eyes, it can be quite the slick operation.
Good luck with it.