Is it permissible to say that al-Husayn died as a martyr?

Yes, al-Husayn (may Allah be pleased
with him) was killed as a martyr. 

That was when the people of Iraq (Kufah)
wrote to him and asked him to come out to them so that they could swear
allegiance to him as their ruler, which happened after the death of
Mu‘aawiyah (may Allah be pleased with him), and the accession of his son
Yazeed to the caliphate. 

Then the people of Kufah turned against
al-Husayn after ‘Ubaydullah ibn Ziyaad was appointed as governor of the city
by Yazeed ibn Mu‘aawiyah and killed Muslim ibn ‘Uqayl, who was al-Husayn’s
envoy to them. The hearts of the people of Iraq were with al-Husayn, but
their swords were with ‘Ubaydullah ibn Ziyaad. 

al-Husayn went out to them, not knowing of
the killing of Muslim ibn ‘Uqayl, or of the people’s changed attitude
towards him. 

Wise men who loved him had advised him not
to go out to Iraq, but he insisted on going out to them. Among those who
gave him this advice were: ‘Abdullah ibn ‘Abbaas, ‘Abdullah ibn ‘Umar, Abu
Sa‘eed al-Khudri, Jaabir ibn ‘Abdullah, al-Miswar ibn Makhramah, and
‘Abdullah ibn az-Zubayr (may Allah be pleased with them all). 

So al-Husayn travelled to Iraq, and halted
at Karbala’, where he came to know that the people of Iraq had turned
against him. So al-Husayn asked the army that came to fight him for one of
three things: either to let him return to Makkah, or to let him go to Yazeed
ibn Mu‘aawiyah, or to let him go to the frontier to fight in jihad for the
sake of Allah. 

But they insisted that he should surrender
to them, and al-Husayn refused, so they fought him, and he was killed
wrongfully as a martyr (may Allah be pleased with him). 

Al-Bidaayah wa’n-Nihaayah
(11/473-520 

Shaykh al-Islam Ibn Taymiyah (may Allah
have mercy on him) said: 

Yazeed ibn Mu‘aawiyah was born during the
caliphate of ‘Uthmaan ibn ‘Affaan (may Allah be pleased with him) and did
not meet the Prophet (blessings and peace of Allah be upon him). He was not
one of the Sahaabah, according to scholarly consensus, and he was not one of
those who were well known for religious commitment and righteousness. He was
one of the Muslim youth, and he was not a disbeliever or a heretic. He
became the caliph after his father died, despite the objections of some of
the Muslims and with the approval of some of them. He was courageous and
generous, and he did not outwardly blatantly commit immoral actions, as some
of his opponents said that he did. 

During his rule, a number of grievous
events occurred, one of which was the killing of al-Husayn (may Allah be
pleased with him). Yazeed did not issue orders that al-Husayn be killed, and
he did not express joy at his killing.  He did not poke the severed head of
al-Husayn (may Allah be pleased with him) with a stick, and the head of al-Husayn
(may Allah be pleased with him) was not brought to him in Syria, but he did
issue instructions that al-Husayn be prevented from achieving his goal, even
if that involved fighting him. But those who received his instructions went
further than that. 

Al-Husayn (may Allah be pleased with him)
asked them to let him go to Yazeed or let him go to the border and keep
watch there, or let him go back to Makkah, but they insisted on taking him
prisoner and ‘Umar ibn Sa‘d issued orders to fight him, and they killed him
wrongfully – him and a number of his family members (may Allah be pleased
with them). His killing was a major calamity, because the killing of al-Husayn,
and of ‘Uthmaan before him, was among the main causes of turmoil in this
ummah, and their killers are among the most evil of people before Allah. End
quote. 

Majmoo‘ al-Fataawa
(3/410-413) 

He also said (25/302-305): 

When al-Husayn ibn ‘Ali (may Allah be
pleased with him) was killed on the day of ‘Ashoora’, he was killed by the
transgressing, wrongdoing group. Allah honoured al-Husayn with martyrdom, as
He honoured other members of his family; He honoured Hamzah and Ja‘far with
martyrdom, as well as his father ‘Ali and others. His martyrdom was one of
the means by which Allah raised him in status, for he and his brother al-Hasan
will be the leaders of the youth among the people of Paradise, and high
status is only achieved by means of trials, as the Prophet (blessings and
peace of Allah be upon him) said, when he was asked which of the people are
most sorely tested? He said: “The Prophets, then the righteous, then the
next best and the next best. A man will be tested to a degree commensurate
with his level of religious commitment. If there is firmness in his
religious commitment, his test will be greater, and if there is any weakness
in his religious commitment, the test will be reduced for him. Trials will
continue to befall the believer until he walks upon the earth with no sin on
him.”

Narrated by at-Tirmidhi and others. 

Al-Hasan and al-Husayn had previously been
granted high status by Allah, may He be glorified, and they did not go
through the same trials and hardships that had befallen their predecessors,
because they were born at a time when Islam was prevalent and they had grown
up with honour and dignity. The Muslims venerated them and honoured them,
and when the Prophet (blessings and peace of Allah be upon him) died, they
had not yet reached the age of discernment. The blessing that Allah bestowed
upon them was that He tested them with that which caused them to join the
other members of their family, just as He tested others who were better than
them. ‘Ali ibn Abi Taalib was better than them, and he was killed as a
martyr. The killing of al-Husayn was an event that provoked turmoil among
the people, just as the killing of ‘Uthmaan was one of the main causes of
turmoil among the people, as a result of which the ummah is still divided
until the present day. 

When al-Husayn (may Allah be pleased with
him) went out and saw that things had changed, he asked them to let him go
back (to Makkah) or to let him go to one of the border regions, or to let
him go and join his paternal cousin Yazeed. But they did not let him do any
of these things, unless he surrendered to them and they took him captive.
They fought him, so he fought back, then they killed him and a number of
those who were with him wrongfully and as martyrs. Allah honoured him with
martyrdom and caused him to join the pure and good members of his family,
and He humiliated thereby those who wronged him and transgressed against
him. End quote. 

Ends.