Helpful ideas for closed fingers around the reins?

You might have open hands because you are trying to be "light" in your contact with the horse's mouth. Understandable, but what results is "weak" contact, not light contact. If you don't have piano hands , then it might be the reins you are using. THick? Won't bend easily?
Think of closing your fingers 'til you can feel the tips of your finger touching the inside of your palm . Then, put your thumb on top and put a little crook in it.
YOu fingers close to form the "house" and your crooked thumb laying on top of them is the "roof" of your house, AND it points directly at the bit, the thumb point is like a laser aimed at the bit rings. Helps to keep that elbow to bit alingnment.

Make the house, put the roof on top, and laser in to the horse's mouth!

OUCH--I have 8 baby chicks in the brooder RIGHT now, 3 days old--DON'T take mine!!
If you horse is safe enough, have you tried "throwing your reins away", then choking up for contact, then follow at the walk, repeat. It's not a really hard concept. I'm sure you've seen people ride with dead hands and hit their horse in the mouth. You might need to psych yourself out on this one.

Tinyliny, I thinks that's exactly it, the reins I use now are completely different then what I usually use. They are really thick, and stiff. I always try to have a connection from the bit to my hands, but maybe it is a little too weak. I'll work on that!

Corporal, can you explain that to me more? What's throwing the reins away..?

Our instincts tell us to curl into a fetal position when we ride and feel off balance. It takes practice to sit up straight, to weight your stirrups and to work your body in sync with the horse while independantly stearing with the reins. We have to practice stretching our arms Forward. Being able to do so enables us to "follow" the motion of the horse's head, which moves regularly at a walk, stabilizes at a trot and reaches with the leading foot at the canter.
Since you do not ask how much pressure it takes to hold the lead while leading your horse, I think you already know how something about closing your hands around the reins. (You have a little mental block, I think, to this.)
If you do the reverse of choking up the reins, and ride with the slack (throwing them away) so you have NO contact, you will be teaching Yourself to use your arms independant of your body. (You alternate between slack, then choke up for contact.)
I have another suggestion but ONLY if your horse is reliable and safe, and I did this to help some of my students. Make a 2nd set of reins out of baling twine. Cut it the length of the two reins and tie to the bit. You will ride with the baling-twine reins on the outsides of your pinkies, while riding the snaffle rein in it's normal position, between your ring and pinkie fingers on both hands. You grip them both, just like when leading your horse. IF you are not following well, the twine will punish your hands--you WILL feel his mouth riding this way!! Hope this helps. It's not really a sin if you have trouble following the mouth. Just switch to riding Western!!! ROFL