The biggest question for me is, can you develop to WP8 with Linux, vim, etc? I just have no plans to install Windows (or OSX) to any of my computers and I don't like to work with any other setup than my customized Linux desktop. But still WP8 looks very exciting.
But all in all, every phone OS (except maybe Firefox OS) puts me down on this. With iOS it's OSX and Xcode and with Android you're better to use some IDE like Eclipse.
If you do a Linux dev environment then you are pretty much stuck with Android. (BTW I'm an Android developer who uses Linux dev environments). You can compile apps from the command line (ant is supported). There are command line tools to do all the device interoperability (eg accessing filesystem, getting logs, installing apps). However it would be unproductive to not use an IDE especially to manage the source files, their contents and locations, and debugging. Java is also very nitpicky due to static typing and the normal Java API paradigm is to never make decisions and always put layers of indirection in front of things. I joke that about half the code I "write" is actually written by Eclipse as I put in what I want and it then doubles the size putting in all the missing pieces, extra syntax, finding completions etc. Such is life with Java. The layout editing tools etc are quite nice especially being able to see previews. Eclipse sucks but it is the least worst solution and you can make working apps with it. You could use vim but you will create a lot of extra work for yourself.
For the iOS work I do I use Xcode. Unbelievably it is slightly less usable than Eclipse (this is not praising Eclipse!). I am constantly astonished at things it does. Presumably eventually Stockholm Syndrome sets in and you train yourself to not do the things that hurt. For a library I am working on that has no gui elements I am actually editing the code on my Linux box using emacs with sshfs access to the files on the mac, and a ssh terminal connection in to build/run/test from the command line. To access the Mac desktop I use Remote Desktop (VNC under the hood). One thing I praise Apple for is that their VNC server implementation is excellent - very snappy especially compared to the dismal Linux experience. Chrome Remote Desktop also works although it sometimes has problems with special keys. I have the Mac sitting in the back of a cupboard with nothing connected except a USB cable that ends up on my desk where I plugin the devices. You can do some things from the command line such as building (xcode-build). I have no idea if you can install apps, get their logs etc using command line tools.
If you don't want to write native apps then you can use PhoneGap. It is essentially a web shell (html widget and javascript) with various extra APIs (eg contacts access) and you provide your code as HTML+javascript. There is much debate about pure HTML5 webapps, solutions like PhoneGap, cross platform tools like MonoTouch versus native apps. Non-native approaches tend to be quicker to initially develop and port, but can have some rough edges and take longer to work at the "edges" of functionality.
TLDR: I have no clue about developing WP8 apps using Linux dev environment
But all in all, every phone OS (except maybe Firefox OS) puts me down on this. With iOS it's OSX and Xcode and with Android you're better to use some IDE like Eclipse.