check the forum list for recent trip report: Whitney Main Trail April. There are pictures of east and west side.

Gives you an idea of conditions at that time. Whitney west side was nearly all cleared off. Kearsage gets plenty of sun on both sides. Forester's steeper south side gets plenty of sun, north side is gentle and can be done no matter what.

Luggy midweight boots would be enough on whatever small area you might encounter. Despite all the hoopla about trailrunners and other tennis shoes, I like to have some grip in all conditions. even a summer hailstorm can change a dry, safe trail.