Is it permissible for a woman to carry or use a bow or a spear?

Praise
be to Allah

Firstly:

At-Tabaraani narrated in al-Mu‘jam al-Awsat (4003):
‘Ali ibn Sa‘eed ar-Raazi told us: ar-Rabee‘ ibn Sulaymaan al-Muraadi told
us: ‘Abd ar-Rahmaan ibn Ziyaad ar-Rasaasi told us: Muhammad ibn Muslim at-Taa’ifi 
told us, from ‘Amr ibn Dinaar, from Ibn ‘Abbaas, that a woman passed by the
Messenger of Allah (blessings and peace of Allah be upon him) carrying a
bow, and the Prophet (blessings and peace of Allah be upon him) said: “May
Allah curse women who imitate men and men who imitate women.”

This is a da‘eef (weak) isnaad. Al-Haythami said in al-Majma‘
(8/103):

This was narrated by at-Tabaraani in al-Awsat from his
shaykh, ‘Ali ibn Sa‘eed ar-Raazi, who is layyin (not very trustworthy), but
the rest of its narrators are thiqaat (trustworthy). Concerning Muhammad ibn
Muslim, al-Haafiz said: He is sadooq (honest) but made mistakes because of
his poor memory.

Taqreeb at-Tahdheeb
(p. 506)

Al-Albaani mentioned his hadith in Da‘eef at-Targheeb
(1256), where he said: It is munkar (odd). End quote.

The reason why it is odd is that al-Bukhaari narrated it in
his Saheeh (5885) from Ibn ‘Abbaas (may Allah be pleased with him)
who said: The Messenger of Allah (blessings and peace of Allah be upon him)
cursed men who imitate women and women who imitate men.

But he did not mention the story of the woman (who carried a
bow). This is the correct and sound version.

Ahmad (6875) narrated that a man from Hudhayl said: I saw
‘Abdullah ibn ‘Amr ibn al-‘Aas whose house was outside the Haram boundary
and the place where he prayed was inside the Haram boundary. Whilst I was
with him, I saw Umm Sa‘eed, the daughter of Abu Jahl, holding a bow and
walking like a man. ‘Abdullah said: Who is this? The Hudhali man said: I
said: This is Umm Sa‘eed bint Abi Jahl. He said: I heard the Messenger of
Allah (blessings and peace of Allah be upon him) say: “They are not of us,
women who imitate men and men who imitate women.”

This is a da‘eef isnaad, because the one who narrated it from
‘Abdullah ibn ‘Amr is unknown. It was classed as da‘eef by the commentators
on al-Musnad, and also by al-Albaani in Da‘eef at-Targheeb
(1257).

Secondly:

A woman should not carry or use bows, swords or spears,
because these are things that men do, unless she needs to do that in order
to defend herself, or if it so happens that she is present at the battle
against the enemy, or there is an urgent need for her to carry them. In that
case there is nothing wrong with her using them and carrying them. But when
there is no need for that, it is not prescribed for her to carry them.

And Allah knows best.