There will be snow. Some resorts seem to close around mid-April no matter what (often it's part of their deal with the National Forest). I'm not as familiar with the South Shore resorts policies, but Alpine will almost definitly be open and I'd bet Heavenly, Kirkwood, and Squaw will be too.
heavenly+squaw should be open unless it stops snowing for the season today. at the very least, squaw likes to try and make memorial day weekend each year and is a great backup just 30 miles from the south shore if heavenly,sierra+kirkwood close. youll have somewhere to ski then for sure.
Don't go to So. shore in April - Northshore either Alpine or Squaw. Normally April means Corn snow in tahoe. The very best is at Squaw because you can start at 0830 on Immigrant in great corn and follow it and the sun right around the mountain stopping at Red
Dog about 1:30 or 2:00 and get a beer. Alpine is ok too. April in Tahoe esxpecially laste April you have to look where the sun is in relationship to the runs. If you have a mt. that only basically faces one direction you are going to have some real ice in the AM and pure slush/slop later. If you can follow thre sun around and follow the good corn snow it can make for some really fun skiing. Good luck with the weather Gods.