https://en.wikipedia.org/wiki/Common_cold#Viruses said:
The common cold is a viral infection of the upper respiratory tract. The most commonly implicated virus is a rhinovirus (30%–80%), a type of picornavirus with 99 known serotypes.[26][27] Other commonly implicated viruses include human coronavirus (≈15%),[28][29] influenza viruses (10%–15%),[30] adenoviruses (5%),[30] human respiratory syncytial virus, enteroviruses other than rhinoviruses, human parainfluenza viruses, and metapneumovirus.[31] Frequently more than one virus is present.[32] In total over 200 different viral types are associated with colds.[3]
Let's disregard the fact that follicle physiology and virology are two, very, very different domains and address the matter at hand, being that there is no cure for the common cold. First of, vaccines exist for almost all known types of viruses, barring some particularities such as the AIDS virus that mutate so often that they end up evading whatever immune response the body can muster.
Vaccines are extremely effective at preventing a viral infection. In theory, there is nothing preventing a vaccine for the common cold to exist. Unfortunately, due to there being at least 100 different sub-types of viruses associated with the
common cold, a practical vaccine is impossible (that is, excluding Influenza for which there are vaccines).
That's for prevention, but what about a "cure"? Well, once again, due to the vast amount of viral sub-types, a medication that would address all of them is not possible at this time. However, a functional cure for the Influenza virus exists in the form of Oseltamivir ("Tamiflu").
https://en.wikipedia.org/wiki/Oseltamivir
So yeah, we can somewhat cure a cold just like we can somewhat regrow a hair follicle. Yay, science?