Won't northern cold air mixing with southern hot air cause major storms/tornados?
Tornadoes, to a small extent, but they're much more common in the spring, when it's the hot air working its way up. There's a small bump in tornadoes in the fall, but it's nowhere near the size you see in the spring.
The colder air working its way down tends to work a little differently. The storms you get out of those tend to be more straight-line. You'd think I'd know exactly why based on what I learned in college, and I probably did even though it's escaping me now, but I can only surmise that it has to do with latitudes: airmasses moving south would be more likely to spread out and north would be compacting. Air compressing into a smaller space would be more likely to rise and convect to make those storms; air spreading out would tend to tamp down any convection. It makes some sort of sense in my head.