You didn't mention your starting point. Since I live in the North, I would recommend the following places for snowfall:
1. Manali (Himachal Pradesh)
2. Auli (Uttarakhand)
3. Shimla (Himachal Pradesh)
4. Munsiyari (Uttarakhand) These places would surely have snowfall during Winters.
Let me know if you have plans other than North, will update regarding the same. :)
You didn't mentioned you place so I may not suggest the nearest place for you but I'll suggest the following place in the month of Mid-Novermber to Mid-February
4. Milam Glacier
Along with site seeing tourists usually love to enjoy snowfall.Adults,kids,people of all different age groups can touch,feel and enjoy the snow.Especially kids love to play games in the snow. There are certain places in Northern India which are famous for snowfall. Auli of Uttarakhand
Pahalgam, Jammu & Kashmir
Manali, Himachal Pradesh
According to your Budget Manali and Spiti are good option to enjoy snow around start of April. Why April so that it is not too cold for you cuz you can get altitude sickness if you are visiting for the first time.
Related Questions For You
Earn credits when your answers are upvoted by others.