>>998546all trails in yosemite are open 365 days a year. the bigger problem will be access to the trailhead. high country will be inaccessible for you because glacier point road and tioga road will still be closed, and big oak flat road connecting 120 to the valley will probably still be closed, so make sure you aren't coming in that way.
it's going to be busy, but you're going to beat summer vacation and the worst of the crowds. honestly if it's your first time i say go full tourist mode and enjoy the valley floor loop. i've been 30+ times in the last 5 years and i still enjoy doing that with first-timers. don't get cute and miss out on the best stuff.
the one under-the-radar thing i suggest is hike up to the base of el cap. it's only about 15 minutes from the road. pic related.
also, ignore any forecast that's more than 3 days in advance. seriously, no one has any idea what they're talking about with the sierra in spring.
finally, webcams and park alerts in one handy place:
>https://www.nps.gov/yose/learn/photosmultimedia/webcams.htm 
