If  you want a bit more flexibility than is offered by Tea House/Homestay trekking but do not have camping equipment with you, it is possible to put together a cheap trekking kit from typical items found in any Indian or Nepali market which will allow you to camp out for a few days.  For shelter you can usually make do with a large plastic tarp, they are used all over India to protect street stalls from rain or as roofs of slum dwellings.  A 10 ft x 10 ft tarp should cost less than 300 INR (about $6 to $7).   This can be used as a roof for one of the many rock walled herder's shelters that can be found throughout the region or as a make-shift tent using rocks or nails as stakes and walking stick as a tent poll, and some rope to tie it down.  A foam pad  for a mattress can also be bought cheaply in most markets.  Look for the places that sell it by the meter.  If you are going to make do with a crude shelter you will need a good sleeping bag, preferably down.  If you didn't bring one from home, the best place to pick one up in the region is Kathmandu, in India try big cities like Delhi and Calcutta which have a few specialized outdoor sports shops, else poorer quality ones can be found in Leh, and Manali.  For food you can make do with dried food or if you are determined to have hot meals relatively small and light but awkward kerosene stoves can be found in every market for around 200 INR to 300 INR.  This style of trekking is best for short trips (3-5 days) up into areas with no villages or lodges, or bridging gaps in homestay treks where you may need to sleep out for one or two nights.  You will probably not want to go out for a few weeks sleeping under a tarp and eating dried food but I'm not saying it can't be done.  However, if you are going to be that far from civilization, it would be best (and safer) to have a more substantial shelter than I've outlined here in case of unexpected bad weather.