In some years the trails open in late or mid May. In many years they do not.
http://www.nps.gov/yose/planyourvisit/tiogaopen.htmNote the opening dates of the Glacier Point Road. The four mile trail will typically open about the same time. The Yosemite Falls trail may open earlier, since it is more exposed and gets more sun.
More often than not, my hiking group plans hikes on those trails in June to August, because they are not open before June. In addition, the Yosemite Falls trail will often close again in spring, not because of winter conditions but because of rockfalls (the only place falling rock in that area has to go is down the trail). That's rescheduled hikes for us before as well.