MySQL DATE field with default CURDATE(). NOT DATETIME

No, you cannot. The documentation is pretty clear on this:

This means, for example, that you cannot set the default for a date column to be the value of a function such as NOW() or CURRENT_DATE. The exception is that you can specify CURRENT_TIMESTAMP as the default for TIMESTAMP and DATETIME columns. See Section 12.3.5, “Automatic Initialization and Updating for TIMESTAMP and DATETIME”.

You can do one of the following:

• Set up a column with a default value for the DATETIME. Create view that extracts the date as a separate column.
• Create an insert trigger to set the date column.