Subdomain basics

Does a subdomain get distributed to the internet DNS system or is it just local to wherever the domain is hosted? Or for a more specific example - I have a domain called "mydomain.com" hosted at "Joe's Webhosting." I create a subdomain called mail.mydomain.com which I redirect to my exchange server which is NOT hosted at Joe's. Now, Joe's service all goes down (must have been the hurricane). Can I still get to my email using mail.mydomain.com?

Thanks,
GGG

 

 

 

 

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