Okay, these ppl were most likely born and raised in Nebraska, so don't listen to them. They are used to that weather and your not.
Bring long sleeved shirts, a hoody and maybe long johns if you can find them in Cali (actually you might wait until you get to Ne to decide on the long johns).
When I go up there in the winter, I bring noted above and also a turtle neck under the shirt.
Buy a cap that goes over the ears and some fleece gloves. It will be cold for you no doubt and if they have the wind that they usually do, you won't like it one bit.
I was raised in Wyo. with the same cold as Ne but I have always hated it. I was an indoors kid when the winter came (5 months out of the year), except to sled and then I looked like the kid in The Christmas Story. I also had 2nd degree frostbite on one of my ears. I really hate the cold.