So long as your well is properly connected, and has been properly maintanined and tested, you should be fine. Talk to your local lender to determine what required to sartisfy these conditions.
Our own house failed the test. we had a water purifier installed at sellers expense before we closed on our property.
FHA requires that your plumbing,heating,electric, roof and basement meet the guidelines. We should think that spring or well won't matter unless it not properly connected.
To be sure ask a mortgage representive, they will be able to provide the correct information for your state.
All the Very Best
Dave & Lisa