In Rails: How is existing data affected by data type change?
I was able to set up a way to test this, and the existing data did convert from DateTime to Date types! As explained here, when doing this with MySQL as the adapter, using change_table triggers the following SQL call:

ALTER TABLE table_name MODIFY COLUMN column_name DATE


Two helpful warnings (courtesy of @SacWebDeveloper):


This is an irreversible change, so if anyone else is trying this and may need to reverse, be sure to use the reversible command or write out the up and down changes.
When converting from DateTime to Date, be aware that rounding uses fractions of a second. Example: '1999-12-31 23:59:59.499' => '1999-12-31', but '1999-12-31 23:59:59.500' => '2000-01-01'.