First and foremost, I'd have to agree with Felix Ungman. If you begin adding in obstacles willy-nilly while keeping the same control style that Tiny Wings has, you'd inevitably end up with frustrating results, leading to an uncontrollable death. However, this could be remedied by adding more reflex controls:

• perhaps, depending on the setting of the game, you could provide a fast dive-bomb downwards or something that would increase speed if you land downhill, but cut your speed if you land uphill.
  
• Another option would be (not having played Tiny Wings), to allow the user to choose to remain on the hill rather than going airbourne. This would prevent the user from being forced into a fatal obstacle. On the flip side, it would be advised to occasionally have grounded obstacles, so that the player couldn't abuse the control.
  

I will say though that this style of game is a painful trend in my opinion. Edmund McMillen (guy who made Super Meat Boy, Binding of Isaac) actually made a game about this sort of thing called AVGM (Abusive Video Game Mechanic, I believe), stating that games today follow the idea of offering a repetitive gameplay for trivial digital items, and also providing a means of simply purchasing the same item with real money as a cop-out from the strain of playing say 50 more rounds. Jetpack Joyride, Farmville, and plenty of other games use this system, and while I don't like it, the foundation of rewarding players for playing is always a good idea, because without it, the game could easily become boring. Just don't make that the foundation of your game.

I guess my point is that innovation is key to separate from the crowds, even if it's something as trivial as LAN-based multiplayer, where others use the momentum-gaining aspect of Tiny Wings to race each other.