If you were to be thrown into an extremely cold environment with tools, there are several things you should do to survive. Winter clothing and shelter would have to be created in order to keep warm. Food and water would have to be obtained to keep yourself from starvation or dehydration. There are many ways in which these could be created or made in order to stay alive.
First, an adequate shelter would have to be created. The tools would hopefully include a shovel and axe to cut tees and and dig a hole for the shelter. This shelter would need to be created quickly so you do not suffer from any potentially harmful side effects from being in the cold. The muscle movement from building the shelter would hopefully keep you warm for the time you have to be exposed while you are creating the shelter. This shelter would also help if it could be placed in the ground. Being under ground would help you stay out of the harsh environment and and would keep the interior insulated. If you create the shelter out of wood, it would also help with insulation and would keep you out of the wind chill.
If possible, you should wear the most layers possible. This is much more effective in staying warm than wearing one large layer. This is because of the air pockets that are created from each layer. The air trapped helps with insulation. If you were not equipped with multiple layers, it would be beneficial to kill an animal with fur and use the fur for warmth. Skinning the creature and wearing the fur side against you would be the best way to keep warm. This is because the fur helps for insulation and the hide helps against strong wind. It would also be imperative to cover your hands, head and feet as this is where most of your bodies heat is lost.
Hunting would be necessary if you were without food. Killing an animal is much more difficult than it sounds and hopefully you would be given tools to do so. Cooking this animal would also be difficult, but not impossible. If you were given a small heater, you would be able to melt snow to get water, and also start a fire to cook any animal you could catch. This fire would help you stay warm as well. If you could not catch an animal, some insects are edible with the removal of the head. There are also some edible plants that live in very cold temperatures.
Living in sub-zero temperatures would be difficult but not impossible. Humans can stay alive in cold weather as long as they have a good shelter, nourishment, and good clothing. With some simple tools, it would be possible to survive.