Yes, Kashmir is very safe and the locals will move mountains to make you feel comfortable. However, weather at this moment might limit your movements. So consider that before you plan a trip.
Except a couple of areas,Kashmir is safe for tourist. Please avoid downtown Srinagar or please avoid places where stone pelting is common. Tourist are never the target but you can easily get caught between the cross fire. The road from Jammu to Srinagar opened yesterday. Snowfall has been continuous and the road availability or accessibility is very uncertain to most of the places.