Physics
Dog Mushing:
Forces act on the sled where the velocity of the dogs minus the frictional force between the sled and snow or ice is equal to the mass of the sled times the acceleration. The frictional force may become larger as the mass of the sled becomes larger because the frictional force is related to the normal force where the normal force of the sled is equal to the gravitational force (gravity acts more as mass increases) acting on the sled.
There is a static and kinetic coefficient for the snow or ice. The ice will have lower static and kinetic coefficients compared to snow's static and kinetic coefficients allowing for the sled to be pulled with a larger velocity as the same force is applied to the sled by the dogs.
The dogs and sled both have kinetic energy when they are in motion. Work is being done by the dogs so power is supplied. Also, there is momentum as the dogs pull the sled. The momentum can become larger as more mass is given to the sled but it will be more difficult to reach a velocity if more mass is given to the sled because momentum is directly related to force multiplied by mass.
Kayaking:
Forces are acting upon the kayak the entire time when it is in water. The water has a density that allows the kayak to float on the water. Also, the kayak's surface area plays a role in the kayak's ability to stay afloat. There is constant pressure applied to the Kayak by the water and by air and by the user of the kayak. Water applies a pressure to the kayak and the kayak applies pressure to the water, Newton's Third Law.
The center of mass of a kayak is important that is if you want to keep dry. A kayak can have a center of mass anywhere along its surface. If the center of mass becomes unbalanced and the kayak is unable to keep stable it will gain energy enough to capsize the kayak.
Drag forces become significant because a drag force can increase the frictional force. To combat drag forces a good design allows for a kayak to minimize its surface area between its bottom and the surface of the water.
Igloos:
Igloos implement a crafty design that equates the net forces of a number of individual blocks of snow to zero. The dome shape igloo directs forces in all directions to equal out to a static equilibrium.
The system's or igloo's center of mass is directed towards the top of the igloo which is then redirected to the blocks of snow below the top. Pressure is acting on the igloo as is gravity.
The igloo holds potential energy due to the force of gravity. A good igloo will not allow for that potential energy to transform into kinetic energy. Therefore, a good igloo will keep you safe from falling snow blocks.
Heat is conserved pretty well in an igloo. The conservation of energy is greatly enhanced due to the first and second laws of thermodynamics. A person's body heat can keep an igloo warm for a fair amount of time. Since snow is a good insulator and a not so good conductor of heat an igloo will keep fairly warm if a candle or oil lamp is lit.
*Bibliography sources 2,3,6