It is important not to confuse taste with flavor. Taste is a sense perceived by special cells that constitute taste buds. When most people use the word taste they are referring to flavor, which is a combination of multiple senses.
Flavor is what people commonly call the "taste" of food. It is
actually a combination of smell, taste, spiciness, temperature and
texture. Much of the flavor of food comes from smell, so that when you
are unable to smell you have lost much of your ability to experience
flavor. -Source
In interpreting flavor the brain takes into account not only taste and smell, but also touch and heat[1]. With spicy food pain is even a factor for flavor.
So, in answer to the title question, no, ~80% of taste is not in the nose, no amount of taste is influenced by smell. Smell is indeed the primary determinate for flavor. I can't find a specific authoritative source for this, however the claim appears repeated in several reputable sources:
Flavor defines the food that is eaten, and is recognized mainly
through the sense of smell.-Source
Researchers say 80 percent of the flavors we taste come from what we
smell, which is why foods become relatively flavorless when we're
plugged up. -Source
It surprised me to read, when I began my research, that about 90% of
what we believe to be taste is really due to smell. -Source
According to Dr Alan Hirsch of the Taste Treatment and Research
Foundation in Chicago, 90% of what is perceived as taste is actually
smell. -Source
It seems fair to say that yes, smell accounts for somewhere around 80% of flavor (taste).