I do get sweaty at night if I am particularly anxious, and my neck is often one of the first places to get it, too! Actually, to think of it, my neck can get sweaty at night regardless of anxiety or not. My body radiates a lot of heat when I'm sleeping, so I'm told.
So I'll wake up with a sweaty neck and dry mouth, etc. because I get so warm.
Like sixpack says, it can be any number of things, and is more likely than not something small like just having too heavy of a blanket. Even if you go to sleep a bit chilly, as your body starts warming up while you're sleeping (and you're still under the blankets) you'll just sweat a bit. Definitely not menopause.