The email templates are set to be Viewable By the entire Organization:
Note that each Template has a Type. The Type is either related to an entity, or it's Global which means this Template is available from anywhere. The out of the box Solution will filter which templates are available to you based on Template Type. Let's take a closer look.
In this example, I want to use the "Won Opportunity Notification (Internal)" email template in a workflow which will run when an Opportunity is Won. First, I open the email template and make changes, if needed, by clicking Insert/Update. Save and Close when finished.
Next I navigate to System ==> Processes to create my workflow. In this example, my first Step is to change the Relationship Type field from Prospect to Customer. The next Step is "Send Email". Select "Use Template" from the list:
Type a description (Send Internal Email). Notice that I have to specify the Template Type. It defaults to Opportunity in this case because we are in an Opportunity workflow. Click Set Properties to continue:
Enter the From/To/Cc/Bcc information. The Template Type is Global, not what I'm looking for:
Change the Template Type to Opportunity Template. Next, check (select) the Won Opportunity Notification Template from the list.
Save, Close and Activate and you're all set.