Actually yes, I have too. Maybe I am just use to it now. It is a dry cold here not sure if that matters. For me personally it is all about hydration. When I am not hydrated I can feel my nose and mouth dry quickly like cotton mouth. Eyes too. I did one time get a nasty sinus infection and the doctor gave a nasal cleaning kit. Which I still use time to time if I feel necessary he explained to me use it whenever I feel like it is needed just not infection.
http://www.swansonvitamins.com/ayr-saline-nasal-rinse-kit-1-kit?SourceCode=INTL405&CAWELAID=509896602&catargetid=530002460000000567&cadevice=c&mkwid=tajrpZ3o&pcrid=18953397607&cagpspn=pla&gclid=CNS9vL7tsbsCFed0QgodoDoAqA
I’m much more of a mouth breather than nose. I have a pretty badly deviated septum so breathing through nose is not that great I’ve found for myself.
For clothing I’ve always been told layers. Put too much on you over heat, comfortable balance. My NCO would tell me be comfortably cold haha. Guess I am little lucky being in military we get issued winter gear. Typically don’t go on very long runs with it being cold as it is. Don’t forget windchill and other weather factors make sure its not freezing rain or something crazy.
When I think about running in morning. I have long sleeve neck shirt, with a jacket wind breaker type. Shorts under, then pants (windbreaker type). I tend not get cold easily compared to others. Maybe its the extra lair of hairy ness hahaha.
Biggest 3 things for me is head,hands and feet. Oh and neck gaiters are really nice. I like to use a thin sock then a thick sock. I’ve seen some people use different shoes, and even thick wool socks or specific socks for winter. Gloves for me I find a insert also called contact glove like wool with another glove to put into it. Depends on how cold it is. Sometimes its overkill and just use inserts. Depends on the day and weather.
Headgear make sure it covers your ears, highly recommend a neck gaiter if its cold enough for it.