I submit that it is part of Indian culture, and that no amount of 'Arabisation' can undo this. For instance, in large parts of our Indian Subcontinent we both speak the same language Hindustani (called Hindi in India and Urdu in Pakistan, though they are almost the same) and culture revolves mainly around language.
Urdu is an indigenous (desi) language, unlike Persian and Arabic which are foreign languages. Let me explain this. The verbs in Urdu (called 'kriya' in Hindi and 'fayl' in Urdu) are all in Hindustani (Urdu being Persianised Hindustani and Hindi being Sanskritised Hindustani), though the nouns and adjectives in Urdu are often in Persian or Arabic. It is the verb which determines to which language a sentence belongs, not the nouns or adjectives (see my article and my talk on YouTube).
We know that Urdu poetry is loved by both Indians and Pakistanis (often members of parliament in both India and Pakistan quote Urdu sheyrs or couplets in their speeches, and mushairas are frequently held in both countries). The verbs in Urdu poetry are invariably in Hindustani (i.e. simple Hindi or simple Urdu which is spoken by the common people) though the nouns and adjectives are often in Persian or Arabic.
Take for instance the sheyr of the greatest Urdu poet Ghalib (who lived in Delhi in India, not in Saudi Arabia):
“Dekho mujhe jo deeda-e-ibrat nigah ho
Meri suno jo gosh-e-naseehat niyosh hai”
Here the verbs 'dekho', 'suno', 'hai' are all in Hindustani.
Similarly one can take the sheyrs of any Urdu poet and they will find the verbs invariably in Hindustani (though the nouns and adjectives will often be in Persian or Arabic). If the verb were to be in Persian, it would become a Persian couplet, not Urdu. And if it were in Arabic it would become an Arabic couplet. This proves that Urdu is an indigenous language of the Indian Subcontinent, and is not a foreign language like Arabic. So how can Pakistani culture be part of Arabic culture?
It is true that the Quran is in Arabic, and that the namaz (salat) is recited in Arabic. But Latin was the language of the Church in Europe for centuries and church services were in Latin, including in France, England, Germany and Spain. Does that make those countries part of Italy?
No doubt Hindus and Muslims have different religions, but for centuries they lived amicably, helping each other, and celebrating each other’s festivals. It was only the British divide and rule policy (see the views of Dr B.N. Pande) which artificially sowed the seeds of hatred in us. However, whenever an Indian (whether Hindu or Muslim) goes to Pakistan, they get tremendous love and affection there, and the same happens when a Pakistani comes to India.
In fact India and Pakistan were one country from the time of Akbar, who in fact had transferred the capital of the Mughal Empire from Agra to Lahore in 1585 (because of the threat from the Uzbek ruler), where he lived for 13 years.
Indians and Pakistanis have many similar food dishes (biriyani etc), attire (like shalwar kameez and sari worn by ladies), etc. The famous Pakistani singer Iqbal Bano wore a sari while singing the revolutionary song "Hum Dekhenge" in 1985 in Lahore Stadium in protest against Gen Zia ul Haq's repressive military rule. Indians and Pakistanis have the same forms of classical music (khyaal, thumri, qawwali, etc)
Indians and Pakistanis living abroad socialise and inter-mix as if Partition had never taken place, and they often help each other. This I have noticed in my trips abroad.
Once I went to Paris with my wife, and while walking on Champs-Elysee I saw 2 young men selling balloons. I thought they were Indians, and started talking with them in Hindustani. They replied in Hindustani: one was from Lahore, and the other from Faisalabad. They said that they were selling balloons because they had to wait for another few months for their work permits, and had to earn some money in the meantime. They were so happy to see and talk to us, as if they had met someone from their own homeland, and they offered us cold drinks.
On another occasion, my wife and I had lost our way in Rome, and a Pakistani, seeing our plight, spoke to us in Hindustani and told us not to worry. He then accompanied us on a bus all the way to our hotel (although his own destination was in the opposite direction). Would an Arab have done this for us? I doubt it. So does Pakistan belong to the Arabic culture or Indian culture?