Does chronic bronchitis cause nose to produce excessive mucus, which is more than mucus coming from throat?

Not usually. Lots of nasal mucus production is usually a sign of allergy, or can be a reaction to cold temperatures and other things. If you are a smoker, you should quit. An ear-nose-throat physician and/or an allergist can do testing to see if allergy or other factors are causing this, and has a number of options in terms of treating it.