I was thinking wooden horns, a bit of small branches with leaves or scales, maybe pupils contracting to slits in strong sunlight. Then there would be psychological effects - failing or lack of restraint in combat, generally short temper, and being somewhat under Forests/Fluttershy's influence (AKA control button under GM's finger). No regeneration or supernatural screech or anything like that, unless given later. 

It could be something that progresses - so the character start out in better condition, and it gets worse - both outside and inside - as the story moves onwards. Sort of undisclosed time limit. 
As for more side effects - I'm open to suggestions ;)