sjcoll's answer is more correct, JHrefugee, although yours would probably be close from a practical standpoint.
The National Forest Service grants the permit for the Jackson Hole Mountain Resort to operate on Forest Service land. It's also complicated somewhat by the fact the the entire northwest boundary of the ski resort borders Grand Teton National Park.
The Forest Service only allows the mountain to operate from the first Saturday of December through the first Sunday of April. The stated reason for those dates has to do, as sjcoll pointed out, with elk, moose, and bighorn sheep migration and calving seasons. Although I have to say that I've never seen an elk or moose much above the valley floor before May and I've *never* seen a bighorn sheep anywhere around the ski area.
It is definitely true that destination skiers quit coming here by the first of April, so even if the Ski Corp *could* legally operate into April, it probably wouldn't make much business sense.
I would disagree about the snow going away that early, though. Last year was unusually warm in March and we still had skiing all the way to the bottom through closing day. It wasn't very good, but the snow was definitely there. In other years, I've gotten annoyed at all the new snow falling into April because it screwed up my spring skiing.
For those of you thinking about coming here in late March, just go ahead and plan it. This mountain has so much variety in elevation and exposure that - if you look a little - you can nearly always find fun, good skiing. I'm a *huge* fan of skiing this mountain the last two weeks we're open.