You can certainly virtualize (if you are currently physical) or move your current virtual machines into the Cloud. V2V migrations can be a pain with device drivers and sometimes I have ended up just migrating JDE via binary, data and registry copies to freshly installed OS images in the new virtual platform. Windows Server 2003 is generally a concern due to it no longer being maintained by Microsoft for security patches but this concern applies wherever you are hosting your machines. Your tools release is too old to support Windows 2008 or anything newer.
There are various ways to mitigate Windows 2003 risks to some degree but the general consensus is that you cannot make yourself fully compliant with various security and regulatory standards and keep running it. I won't lecture you on that as you already have that issue today.
So simple answer again, you can migrate to Cloud and need to secure the deployment as you would any other while keeping in mind the Windows 2003 additional risk factor.