He, sallallaahu 'alayhi wa sallam, would kiss and hold his grandchildren:
Abu Hurayrah said that the Prophet of Allah, sallallaahu 'alayhi wa sallam, kissed Al-Hasan ibn 'Ali when Al-Aqra' ibn Haabis At-Tameemi was present. Al-Aqra' said: "I have ten children, and I have never kissed any of them." The Prophet of Allah, sallallaahu ‘alayhi wa sallam, looked at him and said: "Whoever does not have mercy will not be shown mercy."
This answer to Al-Aqra' shows that kissing one's child is from the parent's mercy, and likewise hugging or smelling them.