What does air "feel" like to a flying mosquito in terms of viscosity? If I go for a walk at, say 4 km/hour, unless there is a breeze blowing, I probably won't notice the air around me at all. If I go for a swim though, I will immediately  notice the viscosity of the water and the effort needed to move through it.
On that sort of scale, I wonder is it possible to estimate how normal still air applies in terms of viscosity,  to a mosquito or other similar sized insect, utilising standard fluid dynamics techniques?
I don't wish to ask a biology based question, or how any insect actually flies, which can be found at Insect Flight. This article implies that insect flight is still a subject of active investigation.

The range of Reynolds number in insect flight is about 10 to $10^4$, which lies in between the two limits that are convenient for theories: inviscid steady flows around an airfoil and Stokes flow experienced by a swimming bacterium. For this reason, this intermediate range is not well understood.

Instead I wonder do we know, compared to the human experience with respect to  the fluid viscosity difference between still air and water, what air "feels" like to move through for an insect, such as a mosquito? 
In other words, is it possible to scale up the insect flying "experience" to the human level, and get an idea of what the human equivalent of the viscosity involved is?  I appreciate it may be impossible to answer this question without referring back to the flight dynamics of insects, in which case my apologies  as there may be no current answer.
 A: Viscosity of air will be same for both fly and human. In the case of flies, from the point of view of the fly, it would seem to it that the viscous force is very high as it keeps the fly afloat. In case of humans, such viscous forces are negligible. So we don't notice it. If you want to scale up the insect flying "experience" to the human level, think about a situation in which a force of wind is able to pull you up in the sky (or rather just keep you afloat in air). What happens is that the air's resistive force acting against the downward motion of the body, equals the body weight and keeps you afloat with net force on body = zero.
That's why if you let a little insect fall from a height you will notice that it does not accelerate in the downward direction. The air drag(or resistance) cancels the little weight of the insect and it falls down with a constant velocity.
That kind of experience for a human is only possible when the air drag is able to produce a force of 60 kgf(or whatever your weight is). That's impossible on Earth. So you get a similar (but not exact same) experience with a wind pulling you up.
For the best experience you may put yourself in some kind of a fluid medium of quite a high density than air but less than your body density(not water as its density is higher than your body).
A: What you need to compare when looking at bodies of different sizes and asking how the forces relate, is in general, the Reynolds Number as you included in your question. This is defined as:
$$ Re = \frac{u L}{\nu} $$
where $u$ is the fluid velocity, $L$ is a representative length scale and $\nu$ is the kinematic viscosity of the fluid. This can also be thought of as the ratio of the inertial forces to the viscous forces. So, when this number is small, the viscous forces dominate and when it is large, the inertial forces dominate. 
The hardest part is picking an $L$. In this case though, it's not so bad. Let's assume that a mosquito is approximately a sphere. Adults rarely exceed 16mm in length, so let's just approximate and say they are 10mm long, so as a sphere they would have a radius of 5mm. Let's then take a normal day at standard temperature and pressure (STP) so that the kinematic viscosity of air is $\nu = 15.11e-6$. And let's assume a light breeze, say 5 m/s. This gives us a Reynolds number of (which hey, also matches the range you posted -- good start!):
$$ Re = \frac{u L}{\nu} = \frac{5 \times 0.005}{15.11e-6} \approx 1655 $$
Okay, so now if we want a human to feel the same inertial-to-viscous force ratio, we want to keep the Reynolds number the same. We can pretend a human is a cylinder. And we can further say that an average human is, roughly, 0.4 meters wide which would give a radius of 0.2 meters. We'll assume the Reynolds number is the same and the air viscosity is the same and solve for a wind velocity to give a similar feel:
$$ u = \frac{\nu Re}{L} = \frac{15.11e-6 \times 1655}{0.2} \approx 0.12 m/s$$
Counter-intuitive maybe, but what we're considering here is what velocities are required to feel the same ratio of inertial to viscous forces. 
In this case, we altered the wind speed but we could also alter the viscosity. If we wanted to do that, let's say we held the speed the same, we would get:
$$ \nu = \frac{u L}{Re} = \frac{5 \times 0.2}{1655} \approx 0.0006 m^2/s$$
This number is almost 40 times larger than the viscosity of air. This means that for a human to feel an equivalent set of forces, they would have to be in a 5 m/s flow of something like hot asphalt, SAE 150 gear oil or diesel fuel. None of which sounds very pleasant, but honestly neither does flying around as a mosquito.
A: Your thought about feeling the water viscosity seems along the right lines, with the small modification that flight is easier to insects than swimming is to humans.
One consideration, though, is an entity's limbs and their capacity to influence personal position:  Insect legs and antenna may feel less rheological resistance and drag in air than ours would in water, but their wings would cause intense personal-position changes similarly to our legs against the ground.  Insects would feel 'torque-ier' or zippier because they have so much less mass.
A: Just imagine yourself shrunk down to the size of an insect. The air would "feel" the same but because of your mass and because you have no special organs to grip surfaces, you would feel constantly thrown around by tornado level winds caused by the swing of a regular sized human's hand. Insects are specially designed to handle these frequent gusts of wind so it feels "OK" to them but for a human it would feel like a constant barrage of hurricanes.
A: Air viscosity is not enough to be noticed by moving mosquito.  But for it's wings air viscosity is important thing, not because their size, but speed. 
