Nah wet weather is fine. The only time I've slipped off my bike in wet weather was going round a corner on a path covered in squashed leaves, which can get really slippy and really should have been cleared (which they actually did later, and resurfaced that section with grumpy surface so it clearly wasn't just me!).

Cycling in snow is when it gets really sketchy. I have done it (along with many other students in Cambridge) but you have to be very slow and careful and quite a few fell off.