It is my experience that when my hands are supporting my upper body they get numb as described. I put my bike on the trainer for the first time and realized that I was sliding forward and supporting most of my weight with my hands (not good). A few minor adjustments and all is good now. I was told that on a trainer you should be able to go into the drops and in that position be able to let go of the bars altogether and still be able to support your position. I can do this now and the ride is much more comfy.

I second the recommendation for gloves with no padding or little padding as possible.