Inclement weather can best be handled with proper shoe soles. It’s best to choose your type according to functionality and aesthetic, with the former being more important.
Most high-end soles are made of leather, as shown below. They are slightly water repellant because they have been burnished (i.e. sealed through rubbing), but are not immune to water by any means.
The antidote for rainy weather are plastic soles. Wearing rubber soles during rain is preferable to wearing leather. You can easily slip in leather, not to mention damage your soles, since leather absorbs water.
Available in many models and brands, but Dainite or Ridgeway soles are mostly used in classic menswear.
Dainite is a UK company most well known for their studded soles. Having seen and felt them, they are very heavy and sturdy. I can offer no comparison between the Dainite or the Ridgeway as I have no experience wearing either.
There are some thinner Vibram soles to be used for light rain. In general, Dainite will last better than these due to durability and thickness. They also make your sole look thicker, but the bottoms are hardly noticeable unless you cross your legs. Any sole (i.e. thick or thin) with textured bottoms will look more visible.
Alone, these thinner soles are quite flimsy and will eventually wear out. It’s a matter of whether you wish to wear lighter soles, but sacrifice protection. There’s quite a weight difference between studded soles and thin soles.
If you’re uncertain what type of sole you should buy, consider the climate you live in. Does it heavily rain often? Is there snow? If so, I would forget thin rubber and go for a sturdier model.
Even with rubber, I would incorporate a metal toe tap to prevent wear (because rubber wears too). Like leather soles, most rubber soles that eventually wear can be replaced.
All soles above are the work of Hiro Yanagimachi.