I'm going in late April. We've never gone at that time of year. However, I can share what I know from this site and the Unofficial Guide. Historically, crowds have been high through March and most of April due to Spring Break. Those crowds have tended to drop off toward late April and stay reasonable through mid-to-late May.
However, because Easter is so early this year, many school districts in the NE have changed Spring Break to coincide with Passover. Thus, many NE schools are on Spring Break during the third and fourth week of April. After hearing this, DH wanted me to change our reservations to May. The only problem with that is that WDW is starting the CinderCelebration in early May and the place is booked up with media and winners of give-away trips.
On the other hand, I have had no problem booking Priority Seating reservations for the times/restaurants that I desired. Also, there are apparently still rooms available at most WDW resorts in April.
So, will there be crowds? Yes. Will it be as bad as going Christmas week? No way.
EthansMom