Helmet quality vs sick sinuses

At the beginning of my motorcycle adventure, I bought a very cheap HJC CS-15 helmet. I noticed that on colder days, even with the ventilation closed, cold air blows on my forehead/ sinuses - which then have a problem with. This season want to buy a better, decent helmet and I wonder if the more expensive models protect the sinuses against cold air when the ventilation is closed? Of course, on warm days, ventilation is highly recommended - but, for example, when l go to work in the morning, spring temperatures are around 10-13 degrees in Poland.