I would like to create a side menu in my windows forms application to look something like the spotify and itunes style (See image as example) What is the best way to achieve this? I want to use icons and have no style limitations.. Was thinking of just using a webbrowser control?

I will strongly encourage you to not use Winforms due to its serious limitations with custom styling, and suggest you to better go with WPF that way doing the menu you want will take you no more than 1 hour (custom control, some grid with proper icons and labels).
Doing so via HTML as you suggest also seems a lot overcomplex (due to back command routing and so on).