The current weather is certainly uncommon, but hardly outside the expected range: 1947 was much worse. And it's got nothing to do with climate change because, as you so rightly say, weather =/= climate.

As for the Maxwell-Boltzmann distribution, I'm no climatologist but I'm pretty sure the atmosphere isn't an ideal gas close to thermodynamic equilibrium, so it really has no application here. And activation energy is the energy required for a chemical reaction to take place, which is also not relevant to weather.