For the Desert go to Jaisalmer. For the Snowfall go to Sikkim especially North sikkim. For the beaches go to Goa. You can check the pictures of these on my posts on tripoto and then decide yourself where you want to go.
I would suggest Goa as it's the best time to visit,provided you love water and beaches.Also, during this time you will be able to find more affordable hotels, and by mid Oct entry to all the beaches are open,so I am sure you can have more fun with less crowd as compared to peak months Nov - Feb.