Almost got hit by car. How do I cope with this?
It seems your now aware of what it means to have a defensive vehicle operating mentality. With a defensive operating mentality you never assume anything. You wait until another vehicle makes a commitment. For example seeing a signal light on doesn't necessarily mean the vehicle is going to move in that direction. They may have accidentally turned it on or forgot to turn it off. Being on a bicycle means you must have a higher level of awareness for prevention rather than your concern of having the right of way. Good for you for now being aware of this. See your heightened sense of defensive awareness as a good thing. I would also suggest using helmet mirrors and hand signals. This will let you know what's happening behind you without you having to twist your body to look behind you. It'll also make you aware when vehicles are about to pass you. Hand signals will alert other vehicle operators what you intend to do next. I personally use a duel horn system. The lower volume horn on the right is for warning cyclist and pedestrians. The loud rechargeable air horn on the left is for alerting closed compartment vehicles they've come too close to me.
Make this into a learning experience. You regret not having worn your helmet, so make sure to wear it from now on. Bad weather is no reason for not wearing a helmet, quite the contrary, you are much more likely to fall on slippery roads. You claim that you are careful, yet didn't notice a car approaching the intersection from your right on snow covered roads(I assume this because you mentioned the road salt). Cars cannot stop as fast on slippery surfaces, so before entering any intersection, make sure that there are no cars close enough to hit you when you start off. A green light indicates that you can proceed, but it does not protect you from reckless motorists. Next time you have a green light after stopping, look every which way before you venture into the intersection. If you see a car approaching the light, there is a very good chance that he may not be able to stop in time. Where I live, motorists are required by law to use winter tires from Dec 15 until March !5. If that is not required where you live there is every chance that an approaching driver may not be able to stop on a cold day. Cope by learning EDIT: "not having water," What do you mean? In cold weather you need far less water than when it is warm, that is no excuse for inattention on your part. Advice? PAY ATTENTION!. No excuses!
You had a near miss. Be more aware so you don't have such close calls in the future.
Learn how to cycle more assertively. A book like Cyclecraft will help - the author was one of the three people who created the UK's official training curriculum Bikeability.
Pedal not peddle - O Hippie has a cartoon to help explain this. Learn from your mistakes, wear hi viz and your helmet.
It is over. You don't have to cope with it.