What weather conditions are slicks suitable for?
Bike tires are treaded to grab on customers rather than the road. Obviously, different tread patterns will perform differently off road, that is: on earth, mud, gravel, sand, roots..

BUT - contrary to popular belief - on the road, whether it is concrete, tarmac or asphalt, treads will do nothing except offer a slightly slower ride and at the same time, less grip on the surface.

On car tires treads have one main function, and that is to channel away water to allow most rubber possible to be in contact with the road. Because of the broad square profile of the car tire, at higher speeds water is 'caught' by the tire too fast for it to escape to the sides, causing the tire to'float' on the water - hydroplaning. Good tread patterns can reduce this effect dramatically.
A secondary function of treaded tires - at least for most of us who seldom leave the tarmac/concrete - is of(f) course better traction on soft surfaces.
On dry tarmac/concrete treads have no effect at all, other than reducing the contact with the surface. In other words, treading will increase contact with surface driving through a puddle of rainwater, but decrease contact under dry conditions. The treaded tire is a compromise.

If you only own one bike with one set of wheels and you ride this bike year in and out, both on and off the road, then you would need to compromise too. But many of us sports more than one bike; we grab our MTB for trekking and reach for our roadbike/hybrid/city commuter when we're on those hard, smoother surfaces. In the latter case a treaded tire has no positive effect what so ever - even if it rains. Here's why:

Hydroplaning on a bike is virtually impossible. Because of the bike tires narrow rounded profile, water is lead to the sides (like a boat cutting through water), ensuring sufficient contact with the ground.

Then what about the wet surfaces? Those slippery curbstones, road paint, manhole covers? Won't treaded tires help at all? Apart from the placebo effect for some riders, the simple answer - backed by physics - is no. Basically, if the treaded pattern don't leave an impression on the surface, it cannot have any effect in regards to traction. You might add water or oil, still those treads will not help you. The same goes for ice. In fact, the only situation where a (heavily) treaded tire will give you better traction within the city limits might be on some types of snow.

All experiments on traction supports this fact and all tire developers know this, yet when you enter a bike store to buy a set of new tires for your hybrid, you are offered treaded tires over slicks in a ratio of 20:1. Why?
1. because the customer believes in treaded traction
2. the shop owner also believes this
3. the customer wants to chose between different products, and choosing between 20 different types of slicks doesn't seem to be much of a choice.
4. the customer wants something new and improved, and 'hey, you had 20 different types of slicks when I was here last'
5. the tire producers know their customers and to keep them buying their stuff - they offer  "something new and improved". They of course know that less costy than actually researching and developing new stuff, is making slight cosmetic changes to existing designs. Thread patterns in road bike tires most definitely belongs to the department of cosmetics.

So, does that mean that any (no-)treaded tire will do? Well, certainly not! Tire profile, thick vs. thin walls, type of rubber compound - there are many factors that will affect grip and traction, tread not being one of them. Also how much air you pump into a tire will affect this.

For those below zero winter days with ice and snow, however, a set of slicks is not recommended. But that also goes for the other regular threaded tires. The only remedy for icy roads are tires with steel/metal spikes. Unfortunately - these tires suck at anything other than icy/snowy conditions. If you live in a part of the world with cold winters, the best thing to do is loading a second pair of wheels with spiked tires, like Schwalbe Ice Spiker or Nokian Extreme, and swapping wheels when the conditions call for it.

I ride my bike(s) to work and for fun. I have a cheap, old "winter bike" for those to-and-from-work snowy days, but my other two tarmac/concrete/asphalt bikes - an old Colnago and a C.dale Bad Boy never wear anything but slicks. Infact, within city limits, I have used slicks only since the mid '90s. Yesterday I received a new pair of Schwalbe Kojak's (26/fat) for my Bad Boy = full control, come rain or shine.