Apple has created the OS X Human Interface Guidelines, which describes the user interface, and other aspects, ought to behave on OS X. Moreso than Microsoft or other companies, Apple strongly encourages developers to follow these guidelines and I believe that OS X users have an underlying assumption, whether they realize it or not, that an app they use will follow it.
In the preface, Apple says what OS X users are looking for:
OS X users have high standards for the apps they run. Meet these high
expectations by designing a user experience that is enjoyable,
streamlined, easy, and adaptable.
You want people to feel that your app was designed expressly for the
OS X platform.
There are myriad details you need to handle as you design the UI of your app, including choosing the right menu items, naming new windows correctly, and using the appropriate controls in a toolbar. Don’t be tempted to ignore the guidelines that govern the use of these UI elements, because users tend to notice even subtle differences in appearance and behavior.
The document goes into greater detail about what these actual changes are, but notice that it's describing little things like menu items and window names and not sweeping changes like massively simplifying the UI. For instance, it describes that Preferences ought to be in the Application menu, rather than the Edit or Help menu like is commonly done on Windows. Similarly, menu bars in-window and shortcuts activated with the Control key are fine on Windows, but on a Mac you need to use the menu bar at the top of the screen and have shortcuts use the Command key. Violating user interface conventions like that are a sure way to make your app "not belong" on OS X, which Mac users are particularly sensitive to.
I think that Mac users prefer a simple and minimalistic UI just as much as, but not more than, users of other platforms. While it's true that Apple has been trending away from skeumorphism and towards flat UIs, the extent to which this has been done in the most recent version of OS X are not nearly as pronounced as the changes done on iOS 7. At any rate, that's an issue involving custom-designed UIs and seems to match a general trend among user tastes. If you're using system-generated buttons and other UI elements, you'll absolutely be fine as it will render such elements as other OS X apps do (and future-proof it in case Apple changes the style).
However, Mac users are probably a bit less tolerant of bad UIs, which may be part of the "simple" thing you were going for. I think that's more because developers tend to pay more attention to the UIs, in part because of the emphases on the Human Interface Guidelines, so they are just more accustomed to seeing good UIs than bad ones.
So your best bet is to focus on matching the little UI things that are defined by the Human Interface Guidelines. Another great thing to do is to use lots of OS X apps and get a feel for how things are done. Sometimes Apple violates their own guidelines (iTunes is guilty of this), but in general, I think you'll see a lot of consistency and will get a feel for how it's supposed to behave.
I'll add that if you are using a completely custom interface (e.g. custom-drawn buttons that are different than the standard operating system buttons), then you probably are fine on another platform so long as it doesn't violate any expectations OS X users will have. In that case, you shouldn't need to redesign it.
I personally have a cross-platform Java app that uses standard UI elements, so those are automatically drawn by OS X. I only have one code base, but make checks for the target platform at various points (e.g. if on OS X, put the Preferences menu item in the Application menu, else put it in the Edit menu). The user interface has been well received by OS X users, which I take away as meaning that they don't necessarily care about a minimalistic UI, but rather one that is consistent with the OS X Human Interface Guidelines, whether they realize it or not.