I'm guessing you're going up through the Meysan Creek drainage, not climbing one of the rock routes on the east face? If going up the Meysan Creek watershed, you probably want to check with the Whitney Ranger station in Lone Pine to make sure the Whitney Portal Road is open (lots of snow this year). If not its another day (at least) to get to the trailhead. The walk-in to the lakes from the campground area is pretty easy later in spring/summer, its a nice trail cut into the slope. But if the trail is still covered with snow it'll be kind of difficult since you'll be walking through snow on a steep slope. The route up is from the lower lakes (commonly called something like 'grass lake' or 'green lake'), just follow the slope up to the ridge, turn left and walk to the summit. One of the better mountaintop views in the Sierra Nevada Mtns (IMO).
Thanks for the reply. Someone posted some recent photos of Whitney Portal Road on Facebook, and it looks like you can drive more than half-way up to the Portal right now. In November 2018, I did a day-hike up to Grass Lake, so I’m familiar with the route. The main question I have is about the depth of the snow in the steep chute above Grass Lake that leads to the summit plateau. We’re planning to bring along snowshoes, crampons, ice axes, beacons, probes, etc.