There has been a great deal of research on the use of Menthol and other ligands that have an effect on the cold or airflow receptors (TRPM8) and their effects on the respiratory system when inhaled as vapors. Instead of posting a hundred or more pages we will provide links to the original papers and brief outlines.
Data sheet from BSAF chemicals on l-menthol, physical characteristics, medical indications, Pharmacology:
Highly technical review of how l-menthol and other ligands activate TRPM8 receptors and new substances that have a higher specificity to TRPM8:
https://ejournals.library.ualberta.ca/index.php/JPPS/article/viewFile/7459/7181
1994 Study *Menthol is an effective anti-tussive agent in an evoked cough model:
http://europepmc.org/backend/ptpmcrender.fcgi?accid=PMC475243&blobtype=pdf
This alternative medicine review of Eucalyptus oil through inhalation covers most existing uses:
http://www.altmedrev.com/publi
Wearing the Nose Band encourages nose breathing:
http://www.ncbi.nlm.nih.gov/pubmed/18951492
Nose breathing improves oxygen uptake in lungs from both a longer exhalation time and flow of nitrous oxide from sinuses into lungs during inhalation where it produces a vasodilation effect. NO concentrations in the sinuses exceeds that needed for antimicrobial effects in vitro. Nose breathing moves the NO throughout the respiratory system and MAY provide a more rapid recovery from infection: