First of all I should mention that this question is addressing very limited space, though important question too.
The first thing that comes to my mind on this subject that you can consider
temporal information in short time interval. if certain values are changed in certain areas, it may be easier to detect snow.
and second solution is here from National Operational Hydrologic Remote Sensing Center (NOHRSC). they use a supervised image classification algorithm to map snow and clouds.
Snow Can be Distinguished From Cloud at 1.6 m
The 1.6 m wavelength allows significantly improved discrimination
between snow and clouds. At 1.6 m, snow has very low reflectance,
while the reflectance of clouds remains high (Figure 1). Therefore,
both cirrus and optically thick clouds can be directly classified and
distinguished from snow at the 1.6 m wavelength (Warren, 1982). This
has been clearly demonstrated using the operational Landsat Thematic
Mapper satellite, which has a channel centered near 1.6 m (channel 5;
1.57-1.78 m) (Dozier, 1987; Baglio, 1989).
and this image from the same place which shows Satellite channel wavelengths in microns (m), and typical reflectance spectra for snow and clouds.
And results they get: