Let us say an explorer was studying a supermassive black hole and ended up blundering past the event horizon. From my understanding, which may be wrong, the only paths allowed after crossing the event horizon are paths that bring the object closer to the singularity. Therefore, if the hapless explorer faced the direction of travel, would none of the photons ahead of the explorer be able to reach the explorer's eyes?
If there is other infalling matter, then certainly they may be able to see it. A simple example is that if they hold their own hand in front of them, they will still be able to see their hand. This is an example of the equivalence principle, one form of which states that spacetime is always locally flat, so that on small enough scales, gravitational effects are not observable.
The infalling observer may also be able to see things at fairly large distances, if those things fell in at a late enough time. The easy way to tell that this is true is to look at a Penrose diagram.