Yes, you could ship from any big city in India, where there are flights or shipfreight connections to Thailand (or Malaysia.. and I assume you have the carnet, so you could send there as well). Delhi, Mumbai, Chennai, probably Kolkata and many others, too.
The downside is, that it´s in many ways a bureaucratic nightmare to ship out of India – and I have firsthand experience, because I did that by air from Chennai 4 years ago. Do-able, but extremely frustrating
(actually that is why many seem to prefer to ship from/to Nepal rather than India).
I haven´t followed the situation in Nepal, and have no experience from Nepal myself.... but that snow thing does sound a bit strange. Even if it´s true, it probably affects certain areas, and not the whole country.
edit. our shipping from Chennai in -08 explained here (at the end of the 1st part - sorry there´s still some Finnish in between, but shipping stuff is fully in English):