Now we have DataObject like this:

class Record extends DataObject{
private static $db = array('Account' => 'Int(8)');
}
...

And for CMS back-end:

class RecordAdmin extends ModelAdmin {
    private static $managed_models = array('Record');
    private static $url_segment = 'records';
    private static $menu_title = records';
}

I want to make that In CMS back-end users can add and edit objects from Record table ONLY if current date is between 23 and 27.
Else (in other days) write message, that they can't write now.

How to implement it?

You could try the onBeforeWrite() method

See http://doc.silverstripe.org/framework/en/topics/datamodel