Heavy coats, coats that shed late/incompletely (partially)/not at all could be possible signs of Cushings, as others have indicated.
Not all horses have the "classic coat", however (my Cushings horse doesn't).
And although it's generally thought of as an "old horse disease", young horses CAN have it.
It might be worth investigating further. Easier to check it out now - Cushings horses/ponies also tend to be much more prone to founder/laminitis...if you know they have Cushings early on, you can take steps to minimize the risk of founder/laminitis, rather than having to deal with that later. In addition, repro problems may have an underlying basis with Cushings. Weight challenges (both "easy keepers" and "hard keepers"). And so on. Because it is a metabolic issue, Cushings can have any number of possible symptoms or combinations of symptoms (or no visible symptoms at all).
Yes, there are other reasons that the pony may have the coat shedding challenges.
Clipping the coat can help make them more confortable in the warmer weather.
Feed changes might help some, regardless of cause. Cushings medications will help, if the pony has Cushings. Make sure that the pony is wormed regularly, if it isn't already.
Lots of fantastic info on Cushings is on the EquineCushings list on yahoogroups. Even if you don't sign up for the list itself, it might be worth some time invested to sign in and look at the files on the homepage.
Hope that this info is of some help.