No, I'm afraid the author has little say about selecting an artist either. That is the province of the publisher's art director, and to a lesser extent the editor.
Michael Whelan would have been a brilliant choice, of course, but just about the time that A GAME OF THRONES was heading into production, he decided to take a two-year hiatus from cover assignments in order to do some original paintings for galleries.
He may be back to doing covers again now, but once a series has begun with a certain artist, publishers prefer to stick with him, in order to maintain a certain continuity of look. In the case of my series, that means all the future covers will likely be done by the present artists -- Steve Youell in the US and Jim Burns in the UK.