Josh, the Mt Whitney Weather page (link always in the "Feature Topics" box to the left) has a NOAA "Whitney Summit Weather" link at the top.

That link takes you near the Mt Whitney summit. You should be able to zoom in and move that map and click on the Horseshoe Meadows area to get a more specific forecast, but of course it is computer-generated and estimated or extrapolated. But that is, I think, as close as you can get.

Now... I see the NOAA site is not behaving properly as I write this, and is reporting some technical difficulty: The "Forecast At A Glance" icons, hourly weather graph feature, Spanish version, and temperatures in Celsius are temporarily not available for this location for technical reasons. We apologize for any inconvenience.