Question: I have done some basic object oriented programming with C++ (creating a B-Tree, Hashing Algorithms, Double Linked Lists) and I have done small project in C (like making a scientific calculator etc.)

**How different is hardware programming (specifically for micro controllers) from software/object oriented programming in terms of the mindset and "thinking" that the programmer has to have?**

Is one usually considered harder than the other my most people?

With my background (as described above) would I need a lot of preparation for going into hardware programming or can I dive straight in without too much preparation?

Answer: 
You will have to completely abandon the object-oriented paradigm when dealing with most microcontrollers.

Microcontrollers are generally register- and RAM-limited, with slow clock rates and no pipelining / parallel code paths. You can forget about Java on a PIC, for example.

You have to get into an assembly-language mindset, and write procedurally.

You have to keep your code relatively flat and avoid recursion, as RAM limitations can often lead to stack issues.

You have to learn how to write interrupt service routines which are efficient (usually in assembly language).

You may have to refactor parts of the code manually, in assembly language, to implement functionality that the compiler doesn't support (or supports poorly).

You have to write mathematical code that takes into account the word size and lack of FPU capabilities of most microcontrollers (i.e. doing 32-bit multiplication on an 8-bit micro = evil).

It is a different world. To me, having a computer science or professional programming background can be as much of a hindrance as having no knowledge at all when dealing with microcontrollers.
Regarding microcontroller vs OOP programming, they are not something opposites. It is true that all vendor libraries are in plain C, but all platforms support C++ OOP too. Developers can build and do build C++ high level libraries and device firmware on top of that. The good example is Arduino libraries, official and user built - mostly C++ classes. Maybe not all OOP advantages can be fully utilized in embedded environment, but well known C++ vs C advantages are valid here too.

Regarding the mindset and thinking, as noted in other answers, microcontrollers are very resource constrained platforms (specially in RAM, less in speed) - stuff like dynamic memory allocation, C++ exceptions are usually ruled out. Given the right hardware is chosen, it is easy to adopt to these limitations and use other techniques (also widely used in other platforms).

In my view, the harder challenge might be one more extra dimension found in embedded programming - timing. This is because usually embedded software deal a lot with real-time events, strictly timed protocols to drive peripheral hardware and general task itself (these is some parallels in other "high level" platforms too, like multi-threaded applications).

Be prepared to read a lot of datasheets when dealing with new hardware - I guess it could be related to "mindset" question part :) Surely some EE and hardware knowledge would be needed.

Also I would like to note that these days embedded software development doesn't require assembly language. In fact Java (BTW it is OOP by default) is already here and getting stronger (at least for some class of embedded devices, for example IoT devices, it could have very bright future).