1. maybe give a slightly better description for hurricane like forms over oceans or forms from multiple storms coming together. You could use the description of they eye, but that would seem too obvious. Also, for the hurricane, if typhoon is not already accepted, it should be.
2. For snow, maybe say that it forms when temps get to around freezing. At first, I thought you were talking about hail.
3. For the low pressure/high pressure systems, it isn't quite clear enough what you are looking for.
4. For cold snap, please accept arctic blast and cold air outbreak as possible answers.