In film "The Day After Tomorrow", a giant snowstorm seizes the Earth for days and freezes nearly everything. What I want to know is, that is this possible in current Earth climate and geology? It doesn't need to be a snowstorm. Just a storm that has radius of few thousand kilometers and powerful enough to destroy a country's infrastructures.
Storms are a consequence of energy unbalance in the trophosphere. The larger this unbalance, the greater the storm.
The largest perturbation we observe now in our troposphere are hurricanes, which are sometimes strong enough to severely damage infrastructure.
Stronger hurrycanes, also known as hypercanes, are hypothetical.
A hypercane is a hypothetical class of extreme tropical cyclone that could form if ocean temperatures reached 50 °C (122 °F), which is 15 °C (27 °F) warmer than the warmest ocean temperature ever recorded. Such an increase could be caused by a large asteroid or comet impact, a large supervolcanic eruption, or extensive global warming. In order to form a hypercane, according to Emanuel's hypothetical model, the ocean temperature would have to be 48 °C (120 °F). A critical difference between a hypercane and present-day hurricanes is that a hypercane would extend into the upper stratosphere, whereas present-day hurricanes extend into only the lower stratosphere.
Hypercanes would have wind speeds of over 800 km/h (500 mph), and would also have a central pressure of less than 70 kilopascals (21 inHg) (700 millibars), giving them an enormous lifespan. For comparison, the largest and most intense storm on record was 1979's Typhoon Tip, with a wind speed of 305 kilometres per hour (190 mph) and central pressure of 87 kilopascals (26 inHg) (870 millibars). Such a storm would be eight times more powerful than the strongest storms yet recorded.
The extreme conditions needed to create a hypercane could conceivably produce a system up to the size of North America, creating storm surges of 18 m (59 ft) and an eye nearly 300 km (190 mi) across. The waters could remain hot enough for weeks, allowing more hypercanes to be formed. A hypercane's clouds would reach 30 km (19 mi) into the stratosphere. Such an intense storm would also damage the Earth's ozone. Water molecules in the stratosphere would react with ozone to accelerate decay into O2 and reduce absorption of ultraviolet light.