Well, check the borders of military area (vojensky obvod Valaskovce) on the map: mapy.hiking.sk/
It is bounded by gray dashed lines. A friend of mine was tenting inside this area and in the morning there came some tanks and lories with soldiers and he was escorted outside in a completely different direction than he intended to go. It was not a good experience. Even crossing the military area can be dangerous outside the footpaths and roads, since you can hit left munition.

CHKO is not a big deal in general but in case of Vihorlat there is a military training range which is more of a concern.

I wouldn’t worry to sleep in a tent in CHKO at all, just make sure you don’t leave any trash behind.