Natural selection can not be random.
Natural selection involves the probability of survival as a function of the requirements of the organism, as the availability of those requirements change over time.
Those probabilities involve both random and deterministic causes. For example, the probability that a fox can survive in America has random effects of nature, competition of the species, etc. Then humans arrive with guns and bulldozers, and all the probability curves are bent into new shapesm, leading to the decimation of the species.
If it was random, natural selection change the selection, constantly.
This is your interpretation, not the one of Science. Natural selection is not a dithering function of uncertainty. It is a tendency to select out the inferior traits of a population based on changing stresses to that population.
Consistency means under similar circumstances, the result should be close but never always different like random. Ironically, random is an important part of modern evolutionary theory, which is inconsistent with this consistency principle laid down by Darwin. This always bothered me.
To alleviate your concern, I suggest rereading the meaning of
natural selection
The question again is, what is the basis for the consistency of natural selection? It can't be due to the spirit of mother nature or that would make evolution a type of religion. Science needs explanations using basic principles of chemistry and physics which underly complex biological states in flux to create consistent choice under given parameters.
No, Science needs
natural selection to explain the observed phenomena.
One way to answer the question, is natural selection is another way of saying living efficiency under a given set of circumstances. If circumstances change, what defines efficiency might also change. If it is hot, thin fur is more efficient for maintaining body systems. If it is cold, thick fur is more efficient for maintaining body systems. Natural selection will pick the most efficient more often than not.
Efficiency is not random, but requires a sense of consistent order which makes the best use of resources. In engineering, lack of efficiency is connected to entropy. To make the most efficient choice would mean natural selection moves in the direction of lowering entropy; most efficient in terms of environment and bio-systems. An eco-system is very efficent and defines lower entropy compared to a disrupted eco-system that is out of steady state; inefficienct.
Whether the creature lives or dies rests on how well adapted it is to all of the conditions. Efficiency has the meaning attached to a specific problem. The question is, will the adaptation survive the complex set of parameters? The question of fur efficiency may relate to the demand for fur (cold) vs. the cost (nutrients). based on diet alone, animals may allocate energy to more fur in the cold seasons, then shed it warm seasons. Every organism is in a continuous state of negotiating supply and demand for every agent of doom using all available resources to survive.
The next question becomes if natural selection is based on efficiency under a given set of conditions, and higher efficiency means the lowest entropy choice, what is the basis for this push toward lowered entropy? It can't be genetic, since genetic change is assume to be random. This means inefficient and higher entropy. This goes in the wrong direction relative to efficency. This means the genetics are secondary. There needs to be a stronger push that can achieve efficiency even when the DNA is making things less efficient via random change.
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. This does not correspond to Natural Selection, since it is neither a system nor noes it have any of the attributes relevant to a system.
It would be more relevant to determine the entropy of heat exchange across an animal's fur vs. the entropy across scales. But this will not lead you anywhere towards arguing against Natural Selection. It will just confirm what you already know, that the adaptations fit the induced stress.
There is one possible, yet simple explanation, connected to water. One way to visualize this is consider water and oil, which we will shake. The shaking will increase system entropy and disorder. If we let it settle, two phases will appear. We can shake this again and again, the system will continue to lower entropy to form the same two phase order. The consistent loss of system entropy is due to the strong hydrogen bonding forces within the water, which reach lowest free energy,when the entropy of the oil is lowered.
Since life is composed of water and organics, we have this basic oil and water analogies throughout life at all levels, with the hydrogen bonding of water trying to lower the entropy of the organics, so the water can minimize free energy. The result is a steady push of the organic of life dissolved in water into order and efficiency.
The closest connection I can think of with what you are saying and Natural Selection might be abiogenesis. Using your argument, I would posit that first cells succeeded based on their ability to exploit the hydrogen bond and other energy sources provided in the methane-ammonia environment from which they arose.
To assume that the law of entropy contradicts evolution is incorrect, all laws are conserved in Natural Selection, and, in fact, are the underlying causes for life and evolution in the first place.