Rich, yes, I believe the general consensus is that sunny weather is mostly a problem where albedo has been lowered - melt ponds, open water, "wet" ice (i.e. where there has been some surface melt), etc., but this is quite a complex issue, as the angle of incidence, water vapour content of the atmosphere, and various other factors all play a part. Over cold ice with high albedo, cloud cover may in some circumstances be "bad" for the ice, by trapping heat and deflecting incoming solar radiation. There was quite a lot of discussion about this topic a few years back - you may be able to find it. Lots of knowledgeable posters citing a variety of scientific papers came to somewhat conflicting conclusions, depending partly on individual interpretations and partly on assumptions about the parameters. If you can't find that discussion, maybe ask the question somewhere else on the forum, as this isn't about the melting season per se.
As a slight tangent, warm, humid air transported into the Arctic can also cause a lot of melt, because cold air holds less water vapour than warm air, so as the air cools, water vapour condenses into liquid water. This change of state releases large amounts of energy.