Is early to mid-November a good time to do a trek of the Himalayas? Are there treks even available at this time, or is this the off season?

I'll be in Delhi, Jaipur, Agra (and possibly Varanasi) from Nov 4- Nov 15. During this time, I would like to squeeze in maybe a 2-4 day trek of the Himalayas in Himanchal Pradesh or Nepal.
I have never done a trek, so I am a beginner, but I am in decent shape.
What company do you recommend I use to set this up?

Also, which Himalayan area is better for beginner trekking, Himanchal Pradesh, or Nepal?

I am not looking for anything too serious. I just want to do an easy to moderate hike of short duration, so I can view some of the Himalayan peaks from a distance. I'm not actually looking to scale these mountains!

a partner from my firm goes on one of these treks once a year in the summer....he once went around october & said it was much harsher....for a beginner it may be better to do one over the summer....

I was afraid of that. But, I've heard that the weather for trekking in the Himalayas is acceptable until the first half of November, after which it gets too cold and snowy.