I've been hearing all about how if you installed Skyrim to your HDD, It'd basically turn your graphics into a garbled mess. I've been hibernating from the forum due to the negativity, so please don't flame me if this has been asked before. I just want to know if it's safe to install now.

Not yet, with luck the 1.2 patch will fix it, this should hit the week after thanksgiving, whenever that is (I'm British so have little to be thankful for). There is a sticky on the main 360 H&S issues page regarding 1.2.

Technically it is safer when you consider that installing the game mean's your xbox wont overheat and that your disc drive isnt burnt out

I have mine installed for exactly those reason's so for now im putting up with the texture issue, there is nothing unsafe about installing the game it's purely from a visual aspect.