I know the v6 auto tranny is known for failing, but my car only does this when quickly accelerating from a stop (on dry pavement). It makes a thud noise which you can feel. No thud when shifting into gears, no thud when full throttle, no slippage, no long shifts. Also, it did not happen in the snow the other day. ????

I tried moving the motor and the mounts "seem" good. ??????

 

Sounds like a motor mount..Have you stood to the side of the car and observed engine movement while someone alternately revs the engine in Drive and Reverse? (left foot on the brake of course)

 

I haven't done it with two people. Just myself looking under the open hood and the motor didn't seem to move all that much.