I'll be in India from early Sept to mid Oct. I'm looking for trek recommendations in northern India, probably around Ladakh, HP or Uttranchal. Preferred landscape includes snow-capped mountains, glaciers, lakes, and ideally green hills. Something like this would be perfect.

And can I rent tent, sleeping bags and other camping gears at nearby towns? Can I rent pack animals to carry my stuff? Many thanks.

Kulu-Manali-Rotng-Pass are very popular amongst the backpacking trekkers.
There is pin parvati pass, and Gangotri which is a famous pilgrimage place for many indians. The mussorrie area near Dehradun is start of another popular trek. And on the other side in East India - Darjeeling

Hope this gets you started.

Are you looking to do it independently or with a small group? Here's a couple that might at least give you ideas of where to go, even if you prefer to go on your own.

It sounds like you're looking for treks further north than this, but I did a quick 4-day trek to Indrahar Pass (4,330 meters) from Mcleod Ganj last year. There was a glacier, but it wasn't massive. The trail was developed by goat herders. Me and a Swiss guy hired a guide/porter through an agency in town. Authentic North Face sleeping bags and quality tents/mats were inclusive. The food they cooked for us was some of the best I had in all of India.