Download your data from your other host and reupload it to HostHorde via FTP. https://www.hosthorde.com/forums/resources/getting-started-with-ftp.31/ https://www.hosthorde.com/forums/resources/getting-started-with-hosthorde.78/
Yes a FTP client like FileZilla. Downloading / Uploading via the built in file manager is a lot more difficult, there are also file size limits.