One of the most enclosed feelings one can have is when something is wrapped around your head.
Here is what I go through every night:
I'm wearing here my CPAP (Continuous Positive Airflow Pressure) unit, used for treating severe sleep apnea. Which I have, in spades. Pressured air is generated through the unit on the little table to the right, then forced through a hose and into the breather under my nose. A constant stream of air is pushed into my lungs during the night, keeping me from snoring and giving me a steady amount of oxygen in the bloodstream. I'm not claustrophobic so it doesn't bother me in that way, although most mornings my nose if very sore when I wake up, as if I had a bad cold and had been sneezing all night. The soreness does go away fairly quickly, though.
Unfortunately I don't always wear it all the through the night. If I wake up in between two of my sleep cycles, it's sometimes very difficult to get back to sleep. I often end up tearing off the mask and accompanying chinstrap, flinging them to the floor and turning off the air unit - sometimes between 4:30 and 6:30am.
Those early morning hours when I do wake up and cannot get back to sleep, I look like this:
For more information:
My Sleep Study (Feb 2005) - Part 1 and Part 2
Sleep Study Followup