For a man to embrace and hug his daughter, or kiss her on the head or cheek or between the eyes by way of showing compassion, kindness and love is permissible, even if she is an adult, on condition that there be no fear of fitnah or provocation of desire. Excluded from that is kissing on the mouth, which is only for spouses, and which usually provokes desire.
Imam Ahmad (may Allah have mercy on him) was asked: Can a man kiss a woman who is his mahram? He said: If he has come home from a journey and does not fear (temptation) for himself.
Ibn Muflih said: But he should never do that on the mouth, only on the forehead or head.
End quote from al-Adaab al-Shar‘iyyah, 2/256. See also al-Iqnaa‘, 3/156; al-Mawsoo‘ah al-Fiqhiyyah, 13/130
Shaykh Ibn Baaz (may Allah have mercy on him) was asked:
Is it permissible for a man to kiss his daughter when she has grown up and passed the age of puberty, whether she is married or not, and whether the kissing is on her hand or mouth or so on? If she kisses him in those places, what is the ruling?
He replied (may Allah have mercy on him):
There is nothing wrong with a man kissing his daughter, whether she is older or younger, without desire so long as that is on her cheek once she has grown up, because it is proven from Abu Bakr (may Allah be pleased with him) that he kissed his daughter ‘Aa’ishah (may Allah be pleased with her) on her cheek. And because kissing on the mouth may lead to provocation of sexual desire, so it is better and safer not to do that. Similarly, a daughter may kiss her father on his nose or head, without desire. But if there is desire then that is haraam for all concerned, so as to avoid temptation and so as to block means that may lead to immorality. And Allah is the source of strength.
End quote from Fataawa Islamiyyah, 3/78, 79.
Embracing sons and daughters when they are small, hugging them, smelling them and kissing them are all part of the compassions and warmth that people should give in abundance to their children and not deprive them of it, because it is compassion that Allah has created in the hearts of His slaves, and Allah only shows mercy to those of His slaves who are merciful.
We advise fathers and mothers not to deprive them of this parental gesture, because it is a basic psychological need, especially in small children, as is proven in all psychological and educational studies, both contemporary and classical.
It is proven in Saheeh al-Bukhaari (5997) that Abu Hurayrah (may Allah be pleased with him) said: The Messenger of Allah (blessings and peace of Allah be upon him) kissed al-Hasan ibn ‘Ali, when al-Aqra‘ ibn Haabis al-Tameemi was sitting with him. al-Aqra‘ said: I have ten children and I have never kissed one of them. The Messenger of Allah (blessings and peace of Allah be upon him) looked at him, then he said: “The one who does not show mercy will not be shown mercy.”
In Saheeh al-Bukhaari (3704) it also says: al-Bara’ entered with Abu Bakr upon his family -- after he reached Madinah as a migrant. ‘Aa’ishah was lying down as she was suffering a fever. I [al-Bara’] saw her father kiss her cheek and say: How are you, O my daughter?
And Allah knows best.