iOS 7 uses only the Helvetica Neue Ultralight font. I'm sure it doesn't use any seperate font just for the note app.
iOS 7 moves to Helvetica Neue for the system font, with frequent use of the ultra light and light weights of that particular font. Apple is so proud of its change in fonts, it changed the â€œiPhoneâ€ font on the back of the iPhone 5s and 5c to match. Itâ€™s a not so subtle change, and iOS 7 also now places more emphasis on being typographically-centered. Much the same way that color is a theme that runs through iOS 7 applications, typography with a color tint applied is now supposed to define most of the user interface elements on their own.
A new feature is dynamic type (through the new Text Kit set of UIKit classes), which essentially is an accessibility feature that enables users to change the font size bias system wide and in applications that use the UIFont method to get a font size. This automatically adjusts weight, character spacing (kerning) and line height, and seems like an awesome change for users who need larger font sizes for elements to be readable.