Most dreams I've had that were weather related were about Tornadoes, Blizzards, and Floods, especially blizzards. I'm not sure if it's because I've never been through one or what, but for some reason they happen the most even when they have absolutely nothing to do with the dream! In one of my dreams we had a "Snowicane", I don't know what month it was, but it had to have been cold in order for it to change a tropical cyclone into a snow machine.
During a time a few months ago, I started getting mixed feelings about becoming a meteorologist. I had several dreams that week weather related, and there was one that stick out the most in my mind. Here's how it went.
It was a bright, warm and humid sunny spring day at the beach with the friends and some family. In the dream I decided to not become a meteorologist and left it in the dust. I never followed weather and always went with it not knowing. While at the beach one day, everyone was oblivious to the storm brewing. Just across the lake was a supercell thunderstorm gathering strength. It began to march across the lake and before anyone knew what was happening, we we're pelted with large hail, blown away with 70+MPH winds. Then, it hit. An EF5 Tornado reached the area and caused total distruction. I was the only to survive, and showed me what could really happen if I didn't persue weather. It was one of the worst dreams I've had in a while and really was the decision maker for me. This was around the days after the SE Tornado outbreak April 27th. Needless to say, I woke up extremely scared, but thank God it was just a dream right? 
I've never had a tornado dream quite that extreme, but I did have one where it was that powerful, it had to have been to level our house. It's sketchy in my memory right now, but I don't remember there being any hail, rain, or lightning just the wind as a warning signal. I was barricaded in one part of our house while the rest of my family was barricaded in other parts and I once I got out I went to search for them. Pretty scary.