The Countess not triggering battlecry after

Cavalry Horn summons the lowest cost minion in your hand after deathblow, which in my case was The Countess, and it did summon, but it did not trigger the Battlecry!!

Is that the way it is??

Yes…

Battlecries only trigger if YOU play the card from your hand. Cards that put other cards onto the field won’t trigger a battlecry.

This isn’t a bug.

Inien is correct. Battlecries only trigger on minions ‘played’ by you. ‘Playing’ and ‘summoning’ are different. The horn only summons the minion, thus bypassing any battlecry.