Head to Swat valley as it has best access in winters. Other options are Kashmir (you can go till Sharda), Shoogran in Kaghan valley or Hunza in Gilgit-Baltistan.
what is the train fare of AC-Lower from khi- Rwp
3400 for AC Business in Tezgam & Khyber Mail
what about road conditions in those areas
Good to bad to worst.
what about security conditions
No security concerns in Swat, Kaghan Valley, Gilgit-Baltistan, Kashmir & Dir-Chitral.
and what are the temprature, and what things should we bring on tour.
January would be freezing cold with extreme snowfall.
and the minimum budget from Karachi to karachi
Depends on your itinerary