The functionality currently does not exist to move your Azure SQL Data Warehouse instance to a subscription other than the one it was created under. What you can do is move the server that contains the instance to another subscription or resource group. Moving a server will move all Databases owned by that server to the destination subscription. The only limitation is that both subscriptions must exist within the same Active Directory Tenant.
The process will be slightly different depending on if you are simply moving an existing DW instance to a different subscription or if you wish to create a copy, or if you wish to move across regions.
To move an existing server and Data Warehouse to a new subscription without changing region, simply follow the instructions here.
To create a copy of an existing Data Warehouse or move the Data Warehouse to a new region, you will need to add in a geo-restore of the instance
Restore the Data Warehouse to a new server in the same subscription, but in the desired destination region
Move the new server owning the Data Warehouse to the desired subscription.
The same technique in no.2 above can also be used if you wish to move a single instance or a subset of instances instead of every database owned by a server.
If you have any issues with this approach, feel free to contact us @ support any time!