At 2020-04-30T23:00:00 my local time, it will be considered May 1st by your approach.

To use local time (or some other time zone), you can use the following approach:

use DateTime qw( );

( my $now = DateTime->now( time_zone => 'local' ) )
   ->set_time_zone('floating');

my $cutoff_date = DateTime->new(
   year      => $now->year,
   month     => 5,
   day       => 1,
   time_zone => 'floating',
);

if ($now < $cutoff_date) {
   # do stuff
}
[download]

The floating tz is used instead of local since some time zones have days don't have a midnight.