Is there a reason why some soft drinks and juices seem sweeter when you freeze it and then wait for it to melt, and then drink it?

I'll make a guess and say it has to do with the escape of carbon dioxide gas that makes soft drinks acidic. The change in temperature would allow for the gas to escape more easily because it has a much different composition. If you let a soft drink go flat, it tastes like syrup almost.

I don't even have a guess about the juices, though.

They all contain a certain amount of water, which defrosts after the juice or soda. If you drink most of it and then leave the rest to thaw out completely, it will taste watery.