Don't go during January and March because it is winter and the time of heaviest snow fall winter, which will make a number of treks and mountain passes inaccessible for an indeterminate amount of time.

Really? Wikitravel said March was a good time with warmer temperatures again.
It's really the only time in the year I can get a longer time off work, and by then I could have around 2500 spending money saved which according to the (minimal) research I've done so far should be enough.

Late March early April might be okay but there could still be a lot of snow left if your planning on any trekking at slightly higher altitudes. April and may are prime season, snow is gone and monsoons don't come till around June usually.