I hold the opinion that it is permissible to wipe over the turban with wet fingers instead of the head if it is difficult to remove and if it was placed on the head when the person was in a state of purification.
The same ruling applies to a woman wearing a headscarf.
The evidence for this is found in the following hadith related in Sahīh Muslim
from al-Mughīrah b. Shu`bah:
Allah’s Messenger (peace be upon him) lagged behind and I did so along with him. He relieved himself and after doing so he said: “Do you have water with you.”
I passed him a vessel of water and he washed his hands and face. Then he started to roll up the sleeve of his robe from his forearm but the sleeve became too tight, so he brought his arm out from below the robe and tossed the robe over his shoulder. He then washed his forearms. He wiped over his forelock and his turban and his socks.
Afterwards, he got back on his steed and I got back on mine and rode until we came upon some people standing in prayer, being led in prayer by `Abd al-Rahmān b. `Awf. He had already completed a unit of prayer with them. When he realized that the Prophet (peace be upon him) was present, he began to step back, but (the Prophet) motioned to him and he kept praying. When he uttered the salām, the Prophet (peace be upon him) stood up and I stood up with him and we prayed the unit of prayer that we had missed.
The opinion that it is permissible to wipe over the turban was that of Abū Bakr, `Umar, Anas, Abū Mūsā al-Ash`arī, Sa`d b. Abī Waqqās, and a number of Companions. It was also the view of a number of Successors.
Many leading jurists adopted this view, including Ahmad b. Hanbal, Ishāq b. Rāhawayh, Abū Thawr, Dāwūd al-Zāhirī, Ibn al-Mundhir, Wakī` b. al-Jarrāh, and al-Awzā`ī.
However, it is not the view of all scholars. Some jurists are of the opinion that it is only required to wipe over a portion of the head, and they argue that the Prophet (peace be upon him) wiped over a portion of the head and then simply continued over his turban.
However, this argument is unconvincing. Wiping upon the turban is a more specific issue than simply wiping over a portion of the head. The fact that the Prophet wiped over the turban shoes that this is what he intended to do, whether he might have wiped a portion of the head or not.
Please take note that some jurists have expressed the following additional conditions for wiping over the turban than the two I mentioned above:
1. Part of the turban should be secured under the neck, coming from one side of the turban to the other. If not, then it should have a tail-like part handing from the back at least four-finger-widths long.
This is the well-known opinion in the Hanbalī school of law.
Other scholars took exception to this idea. Ibn Taymiyah held that it is permissible to wipe over a turban without a tail. The permissibility for doing so is also related from some of the Companions, including Abū Mūsā al-Ash`arī and `Umar.
2. The turban should cover the area of the head customarily covered by a turban. A little bit of hair that usually can be seen from the sides is not a problem, as are the ears and the sides of the head. It makes no difference if these areas are covered or not covered.
3. The timeframe for wiping over the turban is the same as that for wiping over the socks (one day for residents and three days for travellers). This is the official position of the Hanbalī school of law. Ibn Hazm was of the opinion that there is no such timeframe, and this is another opinion found in the Hanbalī school of law.
And Allah knows best.