Mini problems

All horses are different as well as all feeds. My advice in regards ot how much and how often is to get a feed specialist in.

Where I board, someone comes out a couple times a year and measures the horses and devises a specific plan for each horse.

Your vet is correct that they do need hay available and a grass hay like orchard grass would work very well.   As you know horses are meant to be grazing animals and digestion small meals frequently, i.e grazing.  The problem w/ overweight ponies and minis is that sometimes they will even over eat a high calorie hay. Try and stay away from a high alfalfa hay if they are very overweight because it is calorie dense.
 
One problem you may run into when feeding a grass hay without pasture access is a vitamin or mineral imbalance.  There is no way you can know for sure without having the hay tested.  There is the option of adding a micro nutrient supplement like IR Pellets by Kentucky Equine Research which was designed for horses with metabolic disorders.  It is a very low calorie vitamin and mineral supplement fed at a rate of 120g per day for horses and 60g for ponies/ minis.  That is a very small amount.  Here is the link:
 
http://www.kerx.com/products/IRPellet/

  The  basic principles of feeding minis are no different than a regular horse.  Forage needs to account for the bulk of their diets and be fed at a rate of 1-2% of their body weight per day.  Protein will account for 8-10% of their ration.  Macro minerals(Ca, P and Na) need to balanced and normally supplemented as well as Vit A.  Lets assume a 350# mini for convienience sake.  1/3 of a regular horse would equate to 4-7# forage, 1/2# protein, 7 gms Ca, 5 gms P,  5,000 IU Vit A. 
 
   7# hay is about the equalent of 2 flakes on a 2 string grass bale.  If you take average values for grass hay, the nutrients will be met by the grass hay alone.  But you can't assume that, plus you've stated that some is from last year.  Vit A values decline as the hay ages, if your hay is irrigated with hard water, the Ca values will be higher and if you normally have to add lime and don't the Ca will be lower.  You are also feeding classes of minis that have higher demands than a maintenance one.  The nursing mare will require 2x the protein, energy and Vit A and 3x the Ca and P while the weanling will require about the same amount (as the maintenance) of protein and Vit A but 2x the Ca and P in only 1/2 the calories.
 
  If you ever owned a pony or mini, you know you can't offer them free choice hay or pasture 24/7.  They have a slower, more efficient metabolism and will become obese if allowed to eat their fill.  There is a reason you see more foundered ponies than any other group of equines.  Also, are the weanlings and 3 others fed together?  They have such different needs that they really can't be fed together without the 3 getting more than their fair share.  Changes I would make would be feed mare, weanlings and the 3 in separate groups.  Mare, leave her alone.  It's hard enough keeping weight on when nursing.  Is she getting adequate concentrates to up the protein, Ca and P?  The 3 I would cut back their hay.  Break it down to 2-3 meals per day.  To slow them down, spread the hay all over their pen to make them walk around and "graze" for their dinner.  There is always room for a vit/mineral supplement in their diets as much of the hay is deficient in something (Se is a common one).  This can be provided in a loose form hung on the fence (I offer it this way to everyone not matter what else I am providing)  that they can access free choice or something like the ration balancers (ie Purina's Nature's Essentials)  that are ment to be fed at a rate of about 1/4# per head (mini).  The little ones have trouble eating large quantities of hay so for now, you don't have to be concerned about limiting their hay but are they receiving enough Protein, Ca, P and calories while they are growing?  They can only eat 2-3# of forage a day but need the nutrients of about 10.