Neither the global warming model nor the global cooling model make weather predictions. They make climate predictions, which isn't the same thing. Climate's what you can usually expect at a particular time of year. Weather's what's happening right now.
What the model says
The global warming model says that Earth's slowly warming up, on an average global basis. Some people say it's because of human activity. Others say it's because of natural variation in the sun. It doesn't really matter too much in the model what the cause is. The cause only matters if you're wondering if you've got the ability to slow it down or turn it around, or if it's one of those things that's a lot bigger than you.
But global warming's not really the best name for this model. That's why the biggest mistake people make when it comes to the global warming model is naturally assuming that places all over the world are going to get warmer. That's one of those things that's got some truth to it, but not completely.
What the global warming model says is that on average, more heat is being held in by the atmosphere than ever before. Some places will notice a great deal of difference. Some places won't notice much difference at all. Wind and weather patterns could even mean that some places cool down. The important words are "on average." Heating only shows up when you're looking at the global averages.
What does all that heat do to climate?
Much of that heat gets sunk into the oceans, which can absorb a lot of heat before they start to warm up. If the world's oceans warm up by a degree or so on average, they've absorbed a great deal of heat. There's going to be more evaporation, which means more clouds. That means more coastal rain.
Ocean heat also drives hurricanes, but that's a weird connection. Hurricanes can't form at all unless the top ocean layers have gotten warm enough. Getting warm enough's not really an issue, most summers. There's never been a no-hurricane summer, even if they don't reach the coast.
Tropical storms and mild hurricanes could have more rain to them because of the extra evaporation, which means more flooding, but they don't really get stronger if the ocean's hotter. As long as the ocean's warm enough, the same numbers of tropical storms and low-end hurricanes form, even if it gets a bit warmer. However, those systems last longer and go farther north. That's going to make a real difference to higher-latitude coastal regions.
It's in the really powerful hurricanes that there's really a difference. Where the upper wind shear is favourable, there's no upper air dry layer from the Sahara, and there aren't any high pressure systems in the way, there's going to be a lot more explosive development, the kind that takes a hurricane from Category 1 or 2 to Category 5 overnight.
Global warming doesn't make a difference to any individual tornado. That's weather, not climate. If there's wind shear in a supercell thunderstorm, there's a good chance of tornadoes. If there's not, tornadoes won't form. If the air's a bit hotter and a cold front's coming off the mountains, that's usually not going to make a storm less powerful, but it's not going to make tornadoes if there's no wind shear to begin with.
Let's not forget about all that evaporation. In coastal regions and downwind from ocean trade winds, it's going to rain more. Inland, where the winds are already dry, extra heat just means more water gets lost to evaporation. Inland lakes are going to shrink, because all their evaporation goes downwind to outgoing rivers, right down to the oceans. That means the driest areas just got a lot drier.
Polar ice caps
Here's where it gets tricky. The global warming model means that a lot of sea ice and glacial ice is going to melt. Sea ice isn't going to make any real difference to coastal water levels, but without all that nearby ice, arctic regions are going to warm up fast! Actually, that's already happening. That's going to make their weather completely topsy-turvey until things settle down in a few decades.
The real Great White North's always been known for fierce winds, especially during spring and fall when there's a real clash of temperatures. They're only going to get stronger if the contrasts are greater.
Glacial ice is another thing altogether. That's going to raise the sea levels by quite a bit, meaning more erosion, more hurricane surge, and more flooding during incoming storms. Places that rely on glaciers to feed their rivers aren't going to have those water sources anymore. These kinds of places already don't get regular rain, and now they'll get less on top of not having the glaciers anymore. That means drought.
If the Antarctic ice sheet melts, islands and southern regions are going to warm up even faster than the arctic already is. Right now, all that ice is doing a couple of things. It's cooling the air and surrounding water down directly. It's also reflecting away the sunlight. If it melts, it's going to be doing neither of those things.
Finally, a lot of people are looking nervously at the Greenland glacier and what all that cold water could mean to the Gulf Stream. Could it shut it down completely? In the short term, that's going to mean bitterly cold winters for the northern parts of Europe which were always warmed up before by the tropical Gulf Stream. Long term, that could even lead to Ice Age conditions.
At the same time, all of southern Europe, the Sahara, and the marginal regions around the deserts are going to get even hotter and drier than they were before. That's going to make a mess of local agriculture, let alone local weather.