Firstly, I don't think you made any mistake yet. IIRC, the DMG section about mounts & mounted combat offers some advice for dealing with similar siutations. Basically, you'll have to adjust encounters keeping the draconic support in mind.They want to bring him into combat.
Should I let this happen? If I do, how do I adjust the combats to make them fun and interesting?
I know I made a mistake. I made for a chance of them making a dragon friend. But if there's one thing I've learned being a DM, is that you're not to be an Indian giver (giving things, only to take them back).
Thoughts?
Secondly, and more importantly you'll want to roleplay the dragon appropriately. Sure, they made friends with the dragon but that doesn't mean that the dragon will suddenly turn into a cuddly pet. It's still a dragon and dragons generally expect others to treat them with respect or even as their master. I guess the dragon will also claim most if not all of the party's loot. Otherwise the dragon won't stay friendly for long.
In other words, if roleplayed properly your players will want to get rid of their draconic 'friend' as soon as possible.