Dear Ashok,

if the heavy snow fall has any effect on the monsoon it will be to weaken it or delay its onset, via its impact on the meridional temperature gradient. However many other factors such as ENSO could come into play.

http://www.cnrm.meteo.fr/IMG/pdf/snow-monsoon.pdf

This article may help

Fasullo, J., 2004: A Stratified Diagnosis of the Indian Monsoon—Eurasian Snow Cover Relationship. J. Climate, 17, 1110–1122.

doi: http://dx.doi.org/10.1175/1520-0442(2004)0172.0.CO;2

Very interesting paper on this relationship, also connected to the ENSO.

Normally, Eurasian snow cover is negatively correlated with Monsoon since it blocks the incoming moist air from Indian oceans. But ofcourse, other factors do play their role in controlling this 'impact'.

A vital and interesting question.

Significant effect of snow cover in the Tibetan Plateau on eastern Asian summer monsoon has been found, and when the snow cover is larger, the summer precipitation in northern China will increase. It is also found that there exists a positive correlation between summer precipitation of northern China and all India summer precipitation. therefore, the monitoring of snow cover in the Plateau will be important for the outlook of Indian summer rainfall.