If it is 100,000 degrees at the base of Mount Everest, could it snow at the top?
The short answer is "no."
According to the 2005 edition of World Book Encyclopedia, "Geologist believe the temperature at the center of the earth is about 5500 to 9000 F (3000 to 5000 C). The center of the earth is almost hot as the surface of the sun" ("Earth, p. 23).
So, if rocks can melt at 1800 F. (WBE, "Earth," p. 21), they would melt at the temperature of sun (10,000 F. - WBE, "Sun," p. 975) and your question posits the temperature of the base of Mt. Everest to be 10 times as hot as the sun ...
Ergo: Mt. Everest would not exist, or at best, be a puddle, therefore there could be no snow on top of it.