I've been living in Paris for 10 years. You can never really tell what the weather will be like, since global weather is changing and systems will pass through France very rapidly.
Snow is very rare in February - but really nice when it happens. Most often, there will be freezing drizzle and some light rain - but nothing you can't handle. There might be some ice on the streets in the early mornings, but it's usually gone by noon.
Night falls around 6PM, though there isn't normally much sunshine during the day. The major monuments, including the Eiffel Tower, won't be illuminated until sunset.
Life goes on, people go to work, go out to dinner and museums, etc. The streets won't be deserted at all. The Metro will be full of people until the last trip.
Cafe terraces are required to keep a door or one side of the plastic sheeting open, to ventilate smoke away from their waiters as well as customers. There are overhead heaters which will keep your head warm, but from the waist down, you will be cold. A few cafes provide blankets, but not all do.
If you plan to eat on a terrace, your food will become cold very quickly - it's really best to eat inside.
It seems that your visit coincides with school vacations, which run from 20 February to 7 March. Not many tourists choose to visit when the weather's this bad in Paris, but families who don't go skiing will take kids to museums and expos. There are also visitors from the Southern hemisphere who visit during this time. So while there won't be as many people in line as usual, there will be quite a few.
I would not recommend purchasing advance tickets for the Eiffel Tower, due to the fact that adverse weather conditions will often cause it to close or have restricted access.
If you plan to take a day trip by train, there might be some delays due to bad weather. If your train is delayed, you do have the right to get on the next one with your same ticket.
Provins is an easy day trip and an interesting medieval town:
http://www.provins.net/en/festivals-and-events/whats-on/february.html