Yosemite in spring is fantastic. The waterfalls are at their peak then--in good snow years, which it seems will include the current season, April and June are great as well. Early April can be chilly.
The confusion about snow and ice is that heavy winter snowfall can affect the opening dates of campgrounds on the Tioga Road and the Glacier Point road, which when they are open, serve as overflow campgrounds for the Valley and are beautiful destinations in their own right. Also, if Tioga Pass isn't open (Memorial Day is the usual target date), park access from the east isn't possible. The other access roads are at much lower elevations and are clear year-round. Hwy 140 is the easiest.
I don't know if you have much of a shot at finding a campsite in the Valley this late in the game, but try the private campgrounds just outside the Valley on Hwy 140. There are also a couple of small, primitive Forest Service campgrounds along the Merced river (also on 140) that are rarely booked up, even though they are pretty close to the Park.