I know this is an old thread and that the answer marked as accepted works, but it could be simpler (and simple is better).
Anthony got the idea but failed to mention that one needs to iterate on the grid inside the GroupBox and failed to explain how to get there.
In XAML give a name to the main grid inside the GroupBox control (here assuming you named it "GroupBoxGridName"). This will allow you to search for controls inside this Grid including the controls inside any grid in the main group box grid (recursive).
Then do this in the C# code:
foreach (ControlType myControl in GroupBoxGridName.ChildrenOfType<ControlType>)
{
MessageBox.Show(MyControl.Name);
}
Where ControlType can be general as Control or a defined type like TextBox or ComboBox or whatever.