Well, if you were to duct tape between your hat and collar, no snow would be going down....Seriously, a full brim hardhat and turtleneck helps with the snow going down neck and back thing. There's lots of zippy turtleneck poly tops out there. Oh, the Wisconsinites like to wear a pair of light weight gloves with leather "choppers" (mittens) over the gloves. Out here, I like to wear the insulated rubbery gloves. I carry several pairs cuz they still get wet.
To dry them, I put them over the boot dryer tubes. I haven't had to patch them with purple duct tape ....yet.
Can't wear a turtleneck. Too warm unless sitting on Tractor. I would like a full brim except, I do at times like the face screen on mine.
Duck tape is our friend. I might try taping some sort of flap to the back of the hat. Now if I could only find my purple and pastel rolls, I'll be in business.