Even if the inflation stops or slows down, that's still what "cosmological horizon" means.

This merely implies that if the inflation does stop or slow down, the cosmological horizon will also happen to coincide with "how far a signal could possibly travel until the complete death of the universe / the end of time", for c-bound velocities. If there's an upper bound on the spatial size of the universe, then the cosmological horizon might not exist in reality at this point. If there isn't but it turns out we will never reach maximum entropy, then the cosmological horizon also doesn't exist here.

Fun stuff to think about, IMO.