Question:
Can a man or woman hug/kiss their adult grandchildren?
Answer:
It is permitted for a grandparent to kiss or hug a grandchild of the opposite gender. This applies to a grandfather his son's daughter or his daughter's daughter, and vise versa.
Sources:
Chelkas Mechokek E:H 21-10, Be'er Moshe Y:D 2-37 , Igros Moshe 4-45, Om Ani Coma, bAra K'chama 97.