Edited to ad: In this I was mostly just following my from the sub-post I was responding to in the general context of the OP, I sort of took the bit and ran with it, it's not a really honest response to the original question.
Your first paragraph indicates that you may not fully understand the sorts of weapons systems that are available. I don't have up to date information, and if I did I probably wouldn't be allowed to share it, but there is a class of weapons called "theater ballistic missiles" that includes a sub-category of "Short range ballistic missiles". These range from about 600 miles (1000k) to about 2300 miles (3500k), and are nuclear capable. At those ranges even large nuclear weapons are feasible.
Nuclear Weapons are a bad idea, especially the sort of "Primitive" stuff that (I understand) Pakistan and India have, but they are not the world destroying manifestation of Shiva the Destroyer that popular literature would have you believe. Yes, an all out "exchange" between the US and the USSR would pretty much be a civilization ender, and would stand a significant chance of wiping humanity and most of the rest of the species off the face of the planet.
Pakistan has, according to Wikipedia, about 80 to 120 warheads of unknown effectiveness. India's is about the same size (same source says 80 to 100).
This is a serious concern because that's a lot of extra radiation floating around, but in terms of primary effects (blast, EMP, the worst of the fallout etc.) it's really not a whole lot, and it's pretty far away from major centers of trade, major (for the world and for the "west" areas of critical production (we could easily spin up industrial production lost in other parts of the world). The terrain in Pakistan and much if eastern India (including the disputed Kashmir regions) is really rough terrain and would serve to limit blast, fallout and the spread of contaminated material through blowing winds and drainage--at least much more so than the rest of India.
When you look at the list of tests so far conducted (http://en.wikipedia.org/wiki/List_of_nuclear_weapons_tests) you see well over 2000 tests (admittedly spaced out over a much longer time). This suggests that even if they both emptied their arsenals you would not have a world-wide threat of extinction, just hard times. We in the west would largely be insulated from the worst of it because we have things like water treatment facilities, green houses etc.
The lost of life would be horrific, and the fallout--both nuclear and political--would take decades to deal with, but we would survive rather easily--some rough years, and those of use who believe in modern, pluralistic societies with freedom of speech and religion (or no religion as it were), as well as privacy right etc. would have to stand up and hold forth for all we're worth, but it's not a straight up existential risk.
Unless.
Unless it's another Franz Ferdinand moment.
Now, you can label what comes next "bigotry", or "prejudice", or "experience" or whatever, but:
I believe that India is a fairly stable western-style democracy with several STRONG pressure groups that are at serious odds with each other. I believe that they acquired and field a nuclear arsenal because that's what world powers do, and they believe in the deterrent effect of them. They aren't eager to get in a fight, they want to build their nation up to be a modern, powerful country, sort of an eastern interpretation the modern pluralistic representative democracies we enjoy.
I believe that many people in Pakistan seriously want to join the rest of the world community, and want, as much as most Americans, Europeans and Asians to live a peaceful, commodious life. However there is clearly a large segment--maybe not a majority, but a powerful minority with strong influence in the ISI and in the Pakistan government that has a much stronger belief in Islam and in Islamic mysticism than they do in what we could call "modern, pluralistic societies". This second group of Pakistanis is MUCH more loyal to Islam than to any government here on this planet.
Given those positions, my thinking is that it would be Pakistan to initiate the first strike, and even if they did not, they would not present the conflict as a battle between two nation states, but as a religious battle between the West and Islam--at least publicly. This seems to be their (Islam's) standard response to anything that happened after the Reconquista.
This could:
Cause the muslims in India to rebel and and try to take over the rest of the country. This makes any sort of reconstruction MUCH more difficult, and could cause problems along the India/China border as well.
Cause one of the other Islamic countries in that region to attack, or to escalate their attacks on Israel.
Spread to other Islamic countries causing a more generalized initiation of hostilities against "The West".
Spark riots in urban enclaves in much of Europe, the U.K. and Detroit.
(further) Destabilize Iraq, Libya, Lebanon, Egypt and Tunisia. and any other country (Syria?) that tries to liberalize/modernize (yes, Egypt is questionable at this point, but I'm being hopeful rather than realistic on that front).
This could lead to a serious all-in world war. Fortunately if it breaks out like this probably China and Russia will fall on the same side as the US--in this scenario it's basically the Islamic World v.s. all comers. The problem here is that the vast majority of Europe's energy needs are met from Saudi Arabia and Iran, with potential domestic sources being much smaller than the US. This means that Western Europe stands a very good chance of "going dark" under this scenario--we (the US) would have to scale up our oil and bio-fuel production rather rapidly, and since much of this requires infrastructure that isn't amenable to throwing money at it.
None of those pose--as a first or second effect--an existential risk, but it's going to re-arrange the world stage significantly, and third and fourth order effects could cause other flareups.
What would worry me more would be a Sino-Indian war--There is a history there, both countries are very male heavy at this point (male/female balance is very important for maintaining good social order. If it gets too far out of balance you get violence and related problems).
Should China and India come to blows over stupid shit we (US and Western Europe) wind up in a situation were our two biggest industrial centers (India and China) are in conflict and many nations might wind up taking sides. This could precipitate (as a side effect) the nuclear exchange this thread is based on, but would also have much wider consequences.
Your first paragraph indicates that you may not fully understand the sorts of weapons systems that are available. I don't have up to date information, and if I did I probably wouldn't be allowed to share it, but there is a class of weapons called "theater ballistic missiles" that includes a sub-category of "Short range ballistic missiles".
Then I suggest you read further. The Wikipedia link I gave specifically referenced 'short range ballistic missiles' as part of the Indian arsenal. SRBM is not ICBM. And even if it were; the targets...
Last month I was involved in a conversation thread about what the impact of a hypothetical nuclear war would be on existential risk.
There are many potential nuclear war scenarios which would have varying impacts on existential risk. It's difficult to know where to start to gain an understanding of the long-term of nuclear proliferation.
For concreteness, consider the case of an India-Pakistan nuclear war.
According to Local Nuclear War, Global Suffering by Robock and Toon,
[...]
Note that this would presumably cause some degree of chaos in the developed world.
I have not yet investigated the credibility of the papers' claims. However,
Suppose that an all-out nuclear war between India and Pakistan were to occur and were to result in climate change killing 1 billion people. Then would the probability of a positive singularity increase or decrease and if so why?
This question seems very difficult to answer; maybe altogether too difficult for humans to answer. I welcome responses raising relevant considerations even in absence of a good way to compare the relevant considerations. Please read the linked conversation thread before commentating.