general relativity - View from inside the black hole

If an observer is falling toward a black hole with his face away from singularity then what will he observe after crossing the event horizon?

Nothing.

The reason that why I am asking this question because as far as I know for an outside observer, the falling observer appears to freeze at the event horizon i.e. time appears to stop for the falling observer.

Correct. Gravitational time dilation goes infinite, and the distant observer says the "coordinate" speed of light at the event horizon is zero.

So if the falling observer is able to look outward after crossing the event horizon then he will be able to see an infinite amount of time which is impossible. So what will the observer see after crossing the event horizon?

Nothing. The coordinate speed of light is zero at that location, which means that by our clocks, it takes forever to see anything. So the falling observer hasn't seen anything yet, and he never ever will.

IMHO it's worth reading the mathspages Formation and Growth of Black Holes and paying attention to the frozen star interpretation:

"Incidentally, we should perhaps qualify our dismissal of the 'frozen star' interpretation, because it does (arguably) give a servicable account of phenomena outside the event horizon, at least for an eternal static configuration. Historically the two most common conceptual models for general relativity have been the "geometric interpretation" (as originally conceived by Einstein) and the "field interpretation" (patterned after the quantum field theories of the other fundamental interactions). These two views are operationally equivalent outside event horizons, but they tend to lead to different conceptions of the limit of gravitational collapse. According to the field interpretation, a clock runs increasingly slowly as it approaches the event horizon (due to the strength of the field), and the natural "limit" of this process is that the clock asymptotically approaches "full stop" (i.e., running at a rate of zero). It continues to exist for the rest of time, but it's "frozen" due to the strength of the gravitational field. Within this conceptual framework there's nothing more to be said about the clock's existence..."

The author doesn't favour it, but it squares with what Einstein said about the speed of light varying with gravitational potential. The other interpretation doesn't. And note that Einstein didn't refer to the "coordinate" speed of light. He simply referred to the speed of light. So we can reasonably say that at the event horizon, the speed of light is zero, and that this is why a vertical light beam can't get out. The distant observer sees the infalling observer freeze at the event horizon. But the infalling observer doesn't see himself as frozen, because the speed of light at that location is zero. He sees nothing.

NB: SR time dilation is symmetrical, but GR time dilation isn't. If you and I passed each other in gravity-free space at some relativistic speed, we would each claim that the other's clock was slower. But when we're at different elevations, we both agree that the lower clock is going slower.