The COVID-19 pandemic has altered all aspects of the healthcare system’s organization and impacted patients with head and neck cancer (HNC) who have experienced delayed diagnosis and treatment. The pandemic resulted in the admission of patients with severe dyspnea and a need for tracheotomy due to extremely advanced HNC. This study’s objective was to evaluate the clinical characteristics of two multi-center cohorts, “pre-COVID-19” and “COVID-19”, of HNC patients admitted as emergencies for dyspnea. The therapeutic activity of HNC patients in four University Departments of Otolaryngology was studied over two time periods: September–February 2019/2020 and 2020/2021. A group of 136 HNC patients who underwent a tracheotomy in two-time cohorts, pre-COVID-19 (N = 59) and COVID-19 (N = 77), was analyzed. The mean tracheotomies incidence proportion was 1.82 (SD: 1.12) for the pre-COVID-19 and 3.79 (SD: 2.76) for COVID-19 period. A rise in the occurrence of emergency dyspnea was observed in the COVID-19 cohort, and the greatest increase was seen in the centers with the highest limitations on planned surgeries. In the pre-COVID-19 period, 66% of patients presented with symptoms for more than a month in comparison to 78% of patients in the COVID-19 period (p = 0.04). There was a higher incidence of laryngeal and laryngopharyngeal cancer in the COVID-19 period (63% vs. 75%, respectively). The number of tracheotomies performed under general anesthesia dropped in favor of local anesthesia during COVID-19 (64% vs. 56%, respectively) due to extremely advanced HNC. In the COVID-19 cohort, most patients received a telemedicine consultation (N = 55, 71%) in comparison to the pre-COVID-19 period (N = 14, 24%). Reorganization of the referral system, adjustment of treatment capacity for an increased number of HNC, and a reserve for more extensive resection and reconstruction surgeries should be made in the profile of otorhinolaryngological departments, ensuring future HNC treatment is not hampered in case of a new pandemic wave.