Checking 2 dates against todays date

Question

For date manipulations you should use the DateTime class. Also, dates should be stored in Y-m-d format (if you’re storing them differently you can create the DateTime object from a specified format: http://php.net/manual/en/function.date-create-from-format.php (php 5.3+) – but I recommend storing it in the unambiguous Y-m-d format ).

The following assumes Y-m-d formatin the post meta:

$today = new DateTime( 'now' );
$p_date = new DateTime( get_post_meta($post->ID, '_cmb_training_date', true) );
$p_date2 = new DateTime( get_post_meta($post->ID, '_cmb_training_start_date', true) );

if( $p_date > $today || $p_date2 > $today) {
   // stuff
}

As you mention in the comments. You can also easily obtain year/monthy/day information:

if( $p_date2->format('m') == '01' ){
      //$p_date2 is in January
}