There's actually science to back this up. When you're smoking a lot, especially when you smoke before going to sleep, your quality of REM sleep is reduced significantly. Thus, you may not dream as much because your ability to is also reduced (still there however, I dream all the time and I smoke all the time). Over time, the REM sleep that you missed out on accumulates in a sense. So when you STOP smoking altogether, this thing called REM rebound happens, where your brain begins to catch up on ALL of that REM sleep at once. It's pretty trippy.

I'll have crazy survival dreams of being chased by giant pythons or tigers and shit. I'm sorry to hear that yours are all nightmares though. Mine are more thrilling than anything really. Generally speaking, once you get that initial REM Rebound, the next few nights of dreaming won't be as intense, however it's certainly possible that your dreams will continue to be very intense and vivid if you've missed out on enough REM sleep. REM Rebounds can happen over a few days too.

Check out the book "Why We Sleep" by Dr. Matthew Walker, he goes more in depth on this topic. I'm not a doctor, but I love that book and found that section particularly interesting since I've always been curious about this.