Well, I'm positive that
longer (thus thinner) tyres are better in the wet. I think they really pump the water better. I really like to kart in the wet and it rains heavily around my place, so I'm not sure about the theory, that's the feeling I have.
However,
this is very clear when you drive construction machinery: when the motorgrader still has grip, the loader hasn't.
For those not used to drive heavy machinery, a motorgrader has higher, thinner wheels (to be driven primarily on dirt roads), while a loader has wider, "shorter" tyres, more or less like balloons (to be used in quarries, where you don't want a high pressure on crushed rocks, to avoid punctures).
It is quite dangerous to underinflate a loader and drive it in the wet: as you can imagine, grip is essential in that kind of vehicle. If you don't have grip, you cannot "pick" the material, because the bucket won't "penetrate" the gravel or whatever you're loading. I bumped into a couple of trucks when I drove a loader for the first time on the wet. BTW, this is almost as entertaining as racing...
Motorgrader: good in the rain, thin tyres
Loader: bad doggie (in the rain), wider tyres
I'm not totally sure if this can be applied to racing cars, where speeds are (duh) higher. Even taking that in account, a construction vehicle that is "unbalanced" has lower grip. When you load the bucket, the rear wheels slip easily, so, in the rain you try to load "at once". It's very difficult to complete a partial load, because, once you've loaded partially the bucket, you lose the ability to push into the material you're loading. This doesn't happen in motorgraders, which have the cutting blade more or less in the middle of the machine.
I'm also positive that if the pressure is low (no matter the width of the tyre) you have lower grip, because (I imagine) the tread becomes convex, so it's easier to accumulate water in the "arch" under the patch. This is evident when you drive an underinflated kart.
Actually, I put a couple of extra psi on the tyres in the rain, I'm not sure if this is wise, but it works for me. I also try to steer harder in the rain (altough it doesn't seem logical at first sight): the tyres seem to "bite" better. When you do that you have to be very careful not to touch the ruts (I mean, any channel where water accumulates): if you do that, the kart will lose all the "extra" steering power and you will hydroplane.
I think that's the reason why it's harder to lose grip on a motorcycle: the tyres are "rounded" and thin. I mean, the
cross-section of the tyre is rounded (all tyres are round, of course
).