The reference your instructor made to aquaplaning is not quite correct while 100%N1 gave the best answer.
When it comes to water on runways what counts is friction coefficient.
A dry runway obviously has the best friction coeficient.
When measuring friction when rain starts usually you see a degradation in friction because of the mixing of water with dust and other deposits on the surface to form a slippery, muddy mixture. Depending on how much deposits you have, it can go up to viscous aquaplaning a term describing a situation where you have almost NIL friction coefficient. (As slippery as ice or snow) Not being absolutely correct in terms of aquaplaning it describes a situation where you lock the wheels when you just think of applying pressure to the brakes. This also applies to wet grass runways...
With continuing rain the friction coefficient usually rises again when all the mess has been washed away and can reach relatively high values again. - Still stay on the safe side and make calculations conservatively. (I love the illustration of NigelOnDraft
)
Grooved runways have a high friction coefficient even when wet but that is more a question of texture. A coarse surface brakes better if you have rubber tires. Ask the motorcylce guys about abrasion of different road surfaces...
Aquaplaning is: A situation where you have so much speed AND ENOUGH WATER as to lift the tire completely off the ground. At the onset of aquaplaning you may experience partial aquaplaning (may be the case on a take-off). In a total aquaplaning situation (usually on landing) your friction coefficient is NIL! It may even be the case that wheels do not start turning at all! The problem with real aquaplaning is that it may persist even below the onset speeds.
Again - braking is equal to black ice which means nearly non-existent!
Once you slow down below a certain speed (which can not be determined and may be as low as taxi speed) you will brake normally as if on a wet runway.
Factors are mainly Water depth and speed. To make it a bit more relative - you need quite a lot of water on the surface to get aquaplaning. (Usually referenced as: Standing water)
As for drag: Aircraft tires have a nearly ideal form to reduce drag in water. The footprint looks like a boat and the tire too. So drag is not really helping when it comes to braking unless you put your plane down in knee deep water. Usually those who tried, got rid of their landing gear. If that helped in drag I don't know
More questions on aquaplaning - just ask.
RE: Tiger Moth
Add a plow - that adds braking force on hard baked dirt strips