When buying new construction in Villages, you will use the Villages contract form to purchase. That contract has no mention/contingency concerning a mortgage. As far as the Villages is concerned, you are committed to pay the contracted price on closing day, regardless of where your funds come from.
Since VA does not allow the Veteran to pay certain closing costs (and requires the property meet certain construction/inspection standards), it stands to reason that you cannot use VA loan to buy New Construction.
Conventional mortgagees don't care who pays the costs involved in the loan. They require that the house appraises for value, but closing costs are buyers' unless agreed upon otherwise by Sellers.
Again, The Villages don't care if you get a loan, but their contract doesn't protect you the Buyer in the event your lender can't close on time.
It's a one-way street buying from The Villages!
That's my experience, for what it's worth!