I visited Delhi, Agra, and Jaipur in January 2002. It was in the 50s and 60s but not wet. To me that is north but obviously not as north as Nepal. I remember there being fog that disrupted our flight out of Delhi and comments that it was normal for that time of year.

HTH

www.weatherbase.com for info on all destinations you are considering.

The Kathmandu valley in Nepal has very moderate weather, I've been in November and December. November it felt hot during the day (in the 80s) and at night it was in the 40s. In December, it was cooler in the daytime, low 70s and at night sometimes there was a light frost.

It is almost perfect time to visit North India. Good weather, as mentioned above, and prime tourist season--tourist sites are all open.
Since Nepal is in the mountains, I would keep Nepal toward the end of January/early Feb to give yourself a chance at warmer weather --actually, less chance of winter snowfall.

By late March it is warm in north India and still OK.
Happy planning.