i'm not sure if this is how you would do it. but just from quickly thinking about it, you might be able to get away with an IF in the template around where the post icons are displayed.
so IF certain user group {show icons} else {don't show}
like in the newthread template:
FIND:
REPLACE WITH:
PHP Code:
<if condition="$bbuserinfo['usergroupid'] = 1">
$posticons
</if>
you can change the 1 to whatever usergroup you want to see the post icons.
i think that would work, i'm not sure though. if it does work, then you would have to go through the different templates that have post icons in it and put the same code in place.