Running Server 2003 in the cloud is an increasingly hit and miss proposition.
The cloud providers are more than aware that Server 2003 is no longer supported by Microsoft.
Some cloud providers, for example AWS, allow you to spin up new IaaS VMs running Server 2003. Others, like Azure, haven’t offered Server 2003 as an IaaS VM option since end of support expired. The AWS FAQ on Server 2003 (located here: https://aws.amazon.com/windows/faq/#win2003 ) indicates that Server 2003 at this point is functionally “buyer beware”. AWS will certainly let you run it, but will also make it clear to you that the OS isn’t supported and that there isn’t a great deal that they’ll be able to do if you run into issues that aren’t specific to the fabric they provide.
For most people the lack of cloud support for Server 2003 isn’t a problem. They have no intention of migrating an on-prem instance to the cloud. If they had the budget to migrate from Server 2003, they wouldn’t be doing it to a Server 2003 instance in the cloud.
While there are certainly a good number of existing Server 2003 IaaS in instances in the cloud, it’s likely that most Server 2003 instances are going to be crusty on-prem deployments. That Server 2003 is running on server in the corner that keeps ticking over rather than the shiny new one running as a VM in the cloud.