Hi and welcome to the forum! I am glad that I can help you.
You would like to know the cause of the symptoms that you experience.
Sinusitis is infection of the facial sinus cavities. This condition usually appears with nasal infection. During nasal infection the nasal lining becomes swollen and blocks the passage between the facial sinus cavities and the nasal cavity. As there is active infection, viral or bacterial, the infect enters the sinus cavities and initiates inflammation.
Given the data that you described, you may be experiencing sinusitis. You may consider having bacterial culture with an antibiogram. You may need to be taking antibiotics according to the antibiogram results. Wear a hat during the winter to prevent sinusitis. If you experience similar pain (pulsating pain) as the one you described, but in a period when you don't experience any cold, see a neurologist to rule out migraines.
Please keep in mind that I provide medical information only. I am not able to diagnose medical conditions online. Please contact your doctor for further advice and information about diagnosis and treatment options.