Your gonna want to look at the rubber flapper, it does not have to be stuck open for you to get frost. It could be it is not completely seated on the plastic housing. Get a flashlight, and with the freezer door open, shine the light down the iceshoot, and look up in and check if you can see light.

Get a putty knife or butter knife and use it to pop the front cover off the dispenser. there is a gap underneath. Slide in in that gap and pop it off, disconnect the wiring, then take of the 4 screws from the corners of the housing and slide the assy out. There you have access to that flapper. If the flapper is just coming off a bit you can put it back on, if its deformed, you will need to replace it.

Here you go AP3672582 $5.15

I had the problem with the flapper door not completely closing after dispensing ice cubes. Consequently frost built up in side the freezer with the open flapper letting in outside air until it looked like a blizzard had come. My problem was the solenoid in the door that closes the flapper. When the refrigerator was about 6 years old, the solenoid was rusted so that it was frozen in its coil so it would not shut the flapper. I cleaned rust off of the solenoid with sandpaper and applied lubricant liberally. This lasted two years until the problem reoccured. This time I ordered a new solenoid assembley from GE (my GE uses part # WR62X10020 costing $47.25). We'll see how long it lasts this time. A friend of mine has the same refrig and same problem, but he bought the service contract. His service person says this problem happens often.

In my model, you insert a blunt butter knife blade on the outside of the freezer door below the outside trim of the dispenser. There are two plastic tabs along the bottom of the trim that you must release. Then you can swing out the bottom of the trim plate and remove it, leaving the body of the dispenser still mounted in the door. Then you unmount the touch panel again by releasing the plastic tabs at the bottom and let it hang by it wires. (You might want to disconnect the power beforehand.) Remove four screws, one at each corner of the housing that remains in the door. Then remove the inside plastic housing and see the solenoid inside on the right hand side. Remove the three screws holding the solenoid base and open the flapper door to let the actuator arm release from the solenoid piston. Remove the solenoid cable from the connector. Reverse this procedure to insert a new solenoid.