Looking at what you’ve tried (in your commented code), I think you’re close. I’m going to go out on a limb and guess that your event_date meta field is not stored as a numeric timestamp, which is what you were comparing against. Assuming it is stored as a text date like ‘2012-12-08’ (and if not, it probably should be), here’s what you should add to your $args array:

'meta_query' => array( array(
    'key' => 'event_date',
    'value' => date( 'Y-m-d', $current_year ),
    'compare' => '>=',
    'type' => 'date'
) )

Edit:

Knowing now that your data is stored as a numeric unix timestamp, try this:

'meta_query' => array( array(
    'key' => 'event_date',
    'value' => $current_year,
    'compare' => '>=',
    'type' => 'numeric'
) )

*Note: old answer left in for future readers who may be storing their date as a string.