For snow cover studying, I would suggest you to use Modis, Landsat and ASTER satelite imagery. You can use next websites: http://earthexplorer.usgs.gov/ and http://reverb.echo.nasa.gov/reverb/
Yous can register on this websites (it's free) and download aerial images, for Landsat L5 images you can use 5_4_3 band, for Landsat L8 7_5_3 and for ASTER images 3N_2 band (in ArcGIS software)
It depends your needs. Spatial (and temporal) resolutions of Landsat and MODIS are very different.
For fine scale study I suggest you to consider Landsat and for extensive studies MODIS snow cover product which has daily temporal resolution and is easy to handle. With Landsat you need to handle huge data masses and sparse temporal resolution. But Landsat images are available from the mid 80's (MODIS from the beginnig of the 2001).
Both images are though freely available. Links were posted by mr Tielidze.
Normalized Difference Snow Index (NDSI) is widely used in snow related RS studies. I suggest to get familiar with it.
Fmask is automated cloud/cloud shadow/snow mapping algorithm for Landsat (and sentinel), but I don't think it's the best one when snow is the priority. At least according to my experience many snow pixels are classified as clouds. Fmask is also available as an USGS product.
Go to https://nsidc.org/daac to find a number of snow and ice data products. NSIDC (National Snow and Ice Data Center) has one of 12 Distributed Active Archive Centers (DAACs) that are a part of NASA's Earth Observing System Data and Information System (EOSDIS). The NSIDC site provides information about a large number of snow and ice products derived from satellite and airborne instrument data. You can look at the FAQs and contact the NSIDC user services staff if you have questions about their data holdings.