Gas shouldn't be a problem in Dyer, been through there a dozen times and they always have fuel. Not many travelers go through there, just the local Fishlake Valley residents.
I do know that mud can be an issue in the Toiyabe NF this time of year, slick snot type of stuff, same north of 50 in the Eureka area. Silt in the summer equals mud in the winter. Just keep your eyes peeled in shaded areas and you'll be fine.