A black neck gaiter/Buff would probably be perfect! Look for one or two that will fit the full length of the gap.
I'd recommend searching for a cheap version lol. I linked the first thing that popped up on Amazon.
If you have a merino buff you might not need a turtleneck.
Ya, I think I'll go with 2 shorts and 1 pair of pants. The Buff is definitely on the list for both of us. https://www.amazon.com/gp/product/B009VU2TQI/ref=ox_sc_sfl_title_7?ie=UTF8&psc=1&smid=ATVPDKIKX0DER
I use a wool buff to bike commute in winter in chicago. Worked pretty much all winter last year. Planning to use it this year as well.