Keep in mind though that most such internships at places like IIT, IISc, ISI, TIFR etc. are likely to be unpaid and you will most probably have to bear costs on your own.
The way to getting them is to email appropriate professors that you like and then ask them if you could, given their availability, work with them over winter.
I do not know if there are industrial research internships in India over winter. Most of them seem to be restricted to summer.
Source: When I was a graduate student in ISI, there were 2 students from IISER who worked in our lab for a couple of months over winter (Dec-Jan)