In a heavy snow year, on Memorial day weekend, the MR can have snow all the way from the start of the North Forth...about 9000 feet. In a light snow year snow you can count on snow above Lower Boy Scout Lake...around 10500 to 1100 feet.
This picture was taken on Memorial Day weekend in May 2003. That year the snowfall was running a little above normal.
http://outdoors.webshots.com/photo/1215987825061435028GwhdroThis picture was taken at Iceberg Lake on Memorial Day weekend in May 2004. That year the snowpack was running about 35% below normal
http://outdoors.webshots.com/photo/1216010977061435028KstvkxThis picture was taken from Thor Peak toward Iceberg Lake, Memorial Day weekend 2005...following a very heavy snow year.
http://outdoors.webshots.com/photo/1356299426061435028tJxOaMThis picture was taken from Mt Russell a month later (late June)..looking toward Mt. Whitney It clearly shows a bunch of snow everywhere.
http://outdoors.webshots.com/photo/1382961002061435028XiHbXaAnd finally, ...Memorial Day weekend 2006...snow pack was a little above normal. This picture was taken on the north side of the pinnacle pass, between Upper Boy Scout Lake and Iceberg Lake.
http://outdoors.webshots.com/photo/2482766240061435028BFGaXhYou would need to have ice axes and crampons (and know have to use them) for sure this Memorial day weekend if you want to summit Mt. Whitney up the Mountaineers Route...or any other route