When you are going up Kala Patthar, you will definitely have to have a good pair of insulated gloves, similar to what you would wear to ski in!
Make sure that you have adequate gloves for the journey.  Usually, it is your head, feet and hands that will feel the cold the most!  Therefore, you want to make sure that you purchase good gloves for the trip.  You will want both a pair of liner gloves, as well as a bigger, waterproof, glove.  You will want to be able to put the waterproof glove over the liner, so that if you have to take the bigger glove off to operate a camera or anything, you will still have the liner on.  If the temperatures are freezing, then you do not ever want your fingers exposed.  When you are going up Kala Patthar, you will definitely have to have a good pair of insulated gloves, similar to what you would wear to ski in!  If you know your hands are very cold, maybe consider a pair of insulated mittens.