If trying this on Windows you'd be better to start by downloading the expert bundle as the browser bundle really isn't suitable for what you're trying to do. Of course in Linux everything expert mode ;-) I don't think testing this initially on a cloud provider is a good idea for as it may complicate the network setup.
For getting applications to work through tor, this page is probably a good place to start:
https://trac.torproject.org/projects/tor/wiki/doc/TorifyHOWTO/Misc there are lots of good tutorials out there.
Being able to connect outwards via tor probably isn't going to be enough as you'll likely need to ability for other masternodes/clients to connect directly to you in order to initiate transfers, and they won't be able to connect directly to you via a tor exit node. Also your connection to tor can swap exit nodes frequently so you won't have a consistent IP address.
I think the making this work properly will require setting up a tor hidden service, the hidden service .onion address would then be the 'public' masternode address. This will only allow the masternode to be used for clients running tor, so for full utility for everyone some form of 'real ip address' => .onion address proxy would be needed. Perhaps this could be run on a cloud server with an accessible public IP which then forwards requests to the hidden service via tor - no way to know what the real address of the masternode is, though obviously the proxy setup would be exposed.
Hope that is some help and good luck!