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Mosquitos Have Little Trouble Flying in the Rain
sciencehabit writes with an interesting article about the (surprisingly not well studied) effects of rain on flying insects. From the article: "When a raindrop hits a mosquito, it's the equivalent of one of us being slammed into by a bus. And yet the bug will survive and keep flying. That's the conclusion of a team of engineers and biologists, which used a combination of real-time video and sophisticated math to demonstrate that the light insect's rugged construction allows the mosquito to shrug off the onslaught of even the largest raindrop. The findings offer little aid in controlling the pest but could help engineers improve the design of tiny flying robots."
Bats, unfortunately, aren't so lucky: "...these furry fliers need about twice as much energy to power through the rain compared with dry conditions."
No, your two main assumptions are badly wrong.
(1) The terminal velocities of larger objects is larger, and the effect is significant. The mouse hits the ground at a much lower speed than the horse.
(2) The mouse and horse are not even remotely point particles so you should be considering pressure instead of force. You'd have to divide your 22000 number by the ratio of whatever bits land on the horse at once to the same for the mouse; this would be a fairly large number.
To illustrate very approximately why larger objects have larger terminal velocities, consider two falling spheres of equal density, one of small radius and one of large radius. An object reaches terminal velocity when the energy it gains from gravity is perfectly canceled by the energy it has to give up to move air molecules out of the way. Let's compute each.
Basic physics gives the first line of the following. Constant density and the definition of velocity gives the second, and the formula for the volume of a sphere gives the third.
(energy gained from gravity)
= (gravity constant) * (mass of object) * (distance it fell in a given time)
= (different constants) * (volume of sphere) * (velocity of sphere)
= (different constants) * (cube of radius) * (velocity of sphere)
The other half is more approximate. The first line is pretty much trivial from the setup. The second line is from the formula for the surface area of a sphere and from the basic physics fact that the energy of an object is proportional to the square of its velocity. The rest is algebra.
(energy lost to moving air out of the way)
= (constants) * (amount of air moved per unit time) * (energy imparted to each molecule of air)
= (constants) * [(surface area exposed) * (distance it fell in a given time)] * (velocity of sphere squared)
= (constants) * [(radius squared) * (velocity)] * (velocity squared)
= (constants) * (radius squared) * (velocity cubed)
At terminal velocity, these two are equal. Simple algebra gives the answer from here.
(constants) * (cube of radius) * (terminal velocity) = (constants) * (square of radius) * (cube of terminal velocity)
(constants) * (radius) = (square of terminal velocity)
(terminal velocity) = (constants) * sqrt(radius)
The large sphere has large radius, so large terminal velocity. Incidentally this is the formula from the Wikipedia page I linked, though my assumptions were very, very approximate and are probably different from the ones used to derive it.
The simplified answer was actually the next two sentences in the essay:
'You can drop a mouse down a thousand-yard mine shaft; and, on arriving at the bottom, it gets a slight shock and walks away, provided that the ground is fairly soft. A rat is killed, a man is broken, a horse splashes. For the resistance presented to movement by the air is proportional to the surface of the moving object. Divide an animal’s length, breadth, and height each by ten; its weight is reduced to a thousandth, but its surface only to a hundredth. So the resistance to falling in the case of the small animal is relatively ten times greater than the driving force."
You are debating a single sentence of an essay that is an amazing read to say the least. I highly recommend reading it: http://irl.cs.ucla.edu/papers/right-size.html