Yes, both polar regions are warming much faster than other parts of the globe. This is the reason that what we consider "normal" weather patterns have changed. When the Poles are very cold, the Polar Jet Streams are more or less confined to regions close to the Arctic and Antarctic Circles; but now that the Poles are much warmer than normal, the Jet Streams have destabilized, and can reach latitudes closer to the Equator than the Poles. That and warming of the ocean has made tropical and subtropical storms much more common, and much more severe (warmer water releases more water vapor into the atmosphere, and as that turns into water droplets, it releases huge amounts of energy, making the storms much stronger, and with all the extra water, allowing them to dump much more rain onto wherever they are.
For the second part of your question, snow only falls where it is below freezing in some part of the atmosphere, so it always falls in colder climatic zones. Rain can fall anywhere, but snow is confined to regions where high altitudes or naturally cold climates allow it to survive the trip to the ground. That has nothing to do with the warming of the Poles, although the changes in weather patterns noted in the first paragraph can alter where snow falls, by making the air above normally warm areas colder than normal.
Global warming affects the Polar Regions more than other parts of the world. In the past 30 years, temperatures in the Arctic have risen about twice as much as average temperatures on Earth. Temperatures are rising so quickly that the Arctic could have no summer sea ice by 2035. Climate change is amplified in the Polar Regions. The northern and southern reaches of the planet are warming faster than any area on Earth, with the Arctic Ocean and air temperatures rising twice as much as elsewhere. Both the Arctic (North Pole) and the Antarctic (South Pole) are very cold because they get very little direct sunlight. The Sun is always low on the horizon, even in the middle of summer. In winter, the Sun is so far below the horizon that it doesn't come up at all for months at a time. The Polar Regions influence the global climate through a number of processes. As spring snow and summer sea ice cover decrease, more heat is absorbed at the surface. There is growing evidence that ongoing changes in the Arctic, primarily sea ice loss, can potentially influence mid-latitude weather. Temperature decreases progressively from equator towards the poles because it receives less sunlight. As we go away from equator the temperature decreases and in poles it becomes very little or none. As the darkest natural surface on the planet, the ocean absorbs 90 percent of solar radiation. When covered with sea ice, the Arctic Ocean acts like a large reflective blanket, reducing the absorption of solar radiation.Europe and the Arctic are warming fastest, but there are many more people in parts of the Middle East, India, and East Asia that may also warm faster than the rest of the globe. As the planet grows warmer because of climate change, it will not happen evenly. The earth's largest land masses and its north and south poles are warming the fastest, mainly because of differences in how these areas reflect energy from the sun. Rapidly rising Arctic temperatures are driven by a range of processes, including the “surface albedo feedback”, in which melting sea ice uncovers the darker water beneath. This reflects less of the sun's rays back into space, allowing further warming and melting. This is because the air high up in the atmosphere is below freezing. In the simplest terms when the temperature at the ground is less than 32 degrees, the snow will stay snow and when the temperature is above 32 degrees, the snow will begin to melt and fall as rain. The cool air temperature freezes precipitation, and snow falls instead of rain. The cold air also cools that ground so that, when snow falls, it is more likely to accumulate than to melt. At temperatures above about −40 °C (−40 °F), ice crystals form around minute particles of dust or chemical substances that float in the air; at lower temperatures, crystals form directly from water vapour. If the air is humid, the crystals tend to grow rapidly, develop branches, and clump together to form snowflakes. Snowflakes are just collections of ice crystals that cling to each other as they fall toward the ground. Precipitation continues to fall as snow when the temperature remains at or below 32 degrees F from the cloud base to the ground.
Yes, temperatures in the polar regions are changing faster than other regions of the planet. The Arctic has warmed twice as fast as the rest of the world since the late 19th century. This is mainly because the Arctic is covered in ice and snow, which reflect sunlight back into space. As the ice and snow melt, the darker land and ocean absorb more sunlight, which causes the region to warm even more.
The reason why there is snowfall in cold countries instead of rainfall is because the air temperature is below freezing. When water vapor in the air cools to below freezing, it condenses and forms ice crystals. These ice crystals then fall to the ground as snow.
The melting of ice and snow in the polar regions is having a number of impacts, including:
Rising sea levels: As the ice sheets melt, they add water to the oceans, which causes sea levels to rise. This can inundate coastal areas and displace people.
Changes in weather patterns: The melting of ice and snow is changing weather patterns in the polar regions and around the world. This can lead to more extreme weather events, such as heat waves, droughts, and floods.
Loss of habitat: The melting of ice and snow is destroying the habitat of many plants and animals in the polar regions. This could lead to extinctions.
The changes in the polar regions are a serious threat to the planet. It is important to take action to reduce greenhouse gas emissions and mitigate the effects of climate change.