When watching the sky the idea is to be as motionless as possible, so you're not going to generate much heat. A good rule is to assume it's 10 degrees Celsius colder than it actually is. So if it's 5 degrees, dress for minus 5 degrees, etc. Dress like you're going out to play in the snow. Long Johns, pajamas or similar items worn under your regular clothes is a good start, and make sure you've got your warmest gloves, and a hat or balaclava.
Hot drinks are good, too, but avoid caffeine unless there are washrooms handy.
Lie back and relax If you're standing around gazing at something your views tend to be furtive and less than memorable. This is especially true if the object is high in the sky as Comet Hyakutake will be in late March and April, which will make for an awkward neck position. You'll see a lot more if you lie on a blanket on the ground or use a reclining lawn chair. If you're relaxed and motionless you'll notice more details. Bracing your elbows on the arms of your lawnchair or your chest will make all the difference in what you see.