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I always felt pretty sure that's not the correct reading of the rules. That "at the indicated speed" clause makes it ambiguous as that's true of every form of movement--all speeds get reduced by encumbrance. But, apparently, that's how the rules are:
I've been doing some research, and RAW is unclear. I've been unable to find any clarifications of that rule you quoted online, by my own interpretation of it is that "you can't maintain that speed while encumbered by a heavy or medium load", -especially- as they mention that wearing armor doesn't necessarily constitute more than a Light Load in the same paragraph:
Monster Manual 1 said:A creature with a fly speed can move through the air at the indicated speed if carrying no more than a light load; see Carrying Capacity, page 161 of the Player's Handbook. (Note that medium armor does not necessarily constitute a medium load.)
Ergo, to my mind, that means that something like a dragon _CAN_ fly with a medium or heavy load, you just need to calculate how much its fly speed would be reduced, as per the normal "reduced speed for encumbrance" rules.
Those seem to indicate that a dragon like Hunts-The-Ice, (which the OP has quoted as having a Light Load capacity of 200 pounds) could likely take off and carry up to 600 pounds at once, though he'd be struggling to maintain airspeed. His 200ft fly speed (for an Adult White Dragon) would be reduced to a mere 140ft, which would be above his minimum forward speed of "half" (100ft), but not by much, and he'd be really struggling to keep that up.
Disclaimer: I can't recall if the OP has stated if Hunts-The-Ice has a strength-boosting item, but if so, his fly speed would go down with his age category. I picked Adult for this example, because that's the category that has a Strength score of 23, which is required to have a Light Load of 200 pounds.