Is there any type of ritual or prayer that can be practiced on the day of the winter solstice?
Do you talk about it in any of your courses or where can I learn about this?
Yes, all cultures had some ritual, you can look up the ritual of the culture of your preference! The hindus currently do it three weeks late.
YOu can see the effects of the next quarter from the sankranti chart of the winter soltice. Its not a good time to start anything new. three days before and after the winter and summer solstice does not give stability to anything done. Its a time of change, so really only good for spiritual development.
Cast for the capital of the country you are interested in studying. and yes, when the sun is at 0 capricorn. I usuallly use varshaphala techniques to start with but just read the chart based on what you know.
The solstice chart holds until the next equinox.