>Is much of the hill open?
I would think ALL of the hill would be open on an average year. 1st look at the #'s. Go to alta.com and look at snowfall history. Jan, Feb, Mar all get about 90" inches average. April is 73". I would think most of that is in the 1st 20 days of the month. Those April spring storms and instability bring rain most places in the US, but for the Little Cottonwood it is snow. I always remember being there in March and it was a bit warm, there was some precip coming and the local resort guy told me, don't worry, it's not going to rain at the bird in March. It doesn't happen.(i'm sure it has, but not that often).
Last year my last trip stretched into April 2nd. Typical for Snowbird, myself and my 3 kids were skiing in BLIZZARD conditions on our bird day. It was kinda of crazY! at times. On our last day at Brighton it was clear and cold and the snow was just FINE. Not springlike whatsoever. On our day at Snowbasin I was still finding some nice powder on top, but the bottom was starting to deteriorate and get a bit wet, but still quite fine, and they were closing the one gondola, but not because of snow.
So according to the odds, i think you'll be fine. And it would not be unlikely for you to have an awesome powder day. Most likely it'll be in the upper 30's, lower 40's at noon. mid mountain. warm and slow on the bottom, up top should be fine. I would think that on average, conditions are "generally" optimum until April 1st, then they slowly deteriorate.