I personally feel planing to visit kashmir during this winter season is the best option to go for. If u want to go to a place where you can find peace and calmness just as a recreational treat then nothing can beat this option and that too on low budget.
Yes, its totally safe but the roads are jammed every now and then. So, you really need to be aware about the routes when they are open and shut as due to snow as well, people get stuck for hours and sometimes days.