Good subject slicks are great as far as rolling resistance more important is aerodynamics. If the bike is going 20MPH the top of the wheel is going 40Mph.
I don't know that the drag is the major thing you notice, assuming you're supplying the motive power. I've used tires as narrow as an inch on my (non-motorized) on-road bikes and as fat as the 2.3" Big Apples. The main difference is that the fat tires accelerate a lot slower, because they're so much heavier. Once you get rolling though there's really not much difference. I don't really race however, and wind drag issues increase with speed. Cruising at ~15 MPH I can't tell any difference in the wind drag of the fatter tires.
I still run the Big Apples when I will be riding on crushed gravel trails but not otherwise, because the rear 2.3" tire blocks off using the largest cog on the rear wheel. (this is on a long-wheelbase recumbent bike; most "regular" upright bikes won't have this chain-rub issue--but may have fender clearance problems, if you have fenders)
The thinner the tire the smaller the contact patch the more PSI pounds per square inch you can put to the road this translates into traction. ...
Well, no. Racing cars and motorcycles all use
wider tires for better traction, not narrower tires....
This is a 1" tire with 125spi and i have never had a traction issue. rain or snow. but ice is a different story. small patch of ice and your on the ground
...but in bicycling, most people would never notice the difference in traction of a narrow and wide tire, because they never intentionally approach the traction limits of their tires.
***
There's only two times when you really know that you need better traction: straight-line accelerating and while cornering. People don't have enough leg power to spin the rear wheels of bicycles in anything but mud or snow, so straight-line acceleration traction is usually not a problem. With cornering--to approach the limits of your tires' traction you basically have to enter the turn too fast and scrub off speed by drifting (two-wheel-sliding) around the turn. Bicyclists won't do that simply because they're afraid of falling, but also because
speed lost is difficult to regain, so they just slow down entering the turn to where they think they won't lose any speed going around it and spare themselves the (wasted) effort.
~
***(If you watch videos of GP motorcycle racing, they commonly lean the motorcycles over 45º, and then the riders scoot off the motorcycle to the inside as well. A lot of bicyclists tend to think that they corner "about that much", but most get
nowhere near that. Most casual bicyclists won't lean anywhere near that much--less than 5º during casual riding, maybe 15-20º when they're cornering "hard", and most bicycling pros will rarely ever lean the bicycle over more than 30º during a race. The reason racers won't do it is as I said--if you corner hard you slide sideways and lose speed, and in a race, losing speed costs effort. ....On good pavement and with grippy tires you certainly can lean a bicycle over 45º in a turn, but it's pretty terrifying)