Hey Harry,
It is completely possible to do this, using a service like Rackspace you can set up a fairly powerful windows server for as little as $60 a month:
http://www.rackspacecloud.com/cloud_hosting_products/servers/pricing
In my experience using Remote Desktop to log into a Rackspace Windows Cloud Server has been snappy and quick (of course a lot of that depends on the strength of your internet connection). The process of standing up the server is lighting fast, backing it up is even easier, and it can be easily resized down the line if you need more storage/bandwidth.
These days I don't understand why a small to mid sized organization would actually waste capital on server hardware.
Evan