No. However, you can still run legacy HTAs in IE9 mode. For new development using web technologies, Microsoft is recommending a switch to Windows Store Apps.
Here's what Microsoft had to say about HTA support in IE10 and later:
The Internet Explorer team is increasingly focused on standards compliance, and markup-based behaviors are not part of modern web standards. In IE10 mode support for markup based behaviors has been removed, and this includes hta:application.
In addition, for HTML-based applications the focus for Windows 8 and beyond the team's focus is on Windows Store applications.
I suspect that an HTA would work in Windows 10, but only in IE9 mode. (EDIT: It does!) It would be a major shift if Microsoft built Edge with HTA support.
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