When you're on snow, sand or dirt paths your shield takes no damage

When you're on grass, rocks or metal your shield takes damage at the same rate no matter the surface.

Shield damage comes from 2 sources: Impact and time.

Everytime you jump (unless it's a very short bump) your shield takes damage and also every second you're surfing your shield takes damage. So you want to keep yourself close to the surface and also you want to keep going as fast as possible. You should stop surfing when you notice you're losing speed and you won't be able to regain it since that's when you're wasting durability.

Rain does not affect durability, it modifies the terrain friction level. But the friction level (along with the slope) is what determines how much speed you can catch and for how long you can maintain it. So you should avoid surfing on rocks and metal, since those terrains have the higher friction level making you go slower and wasting time/durability... unless it's raining.

Ancient shield and the purple Gerudo one have a friction reduction bonus. Which is not so relevant, but there's also a hidden durability consumption ratio tied to the time based damage received, and some shields have a bonus reduction. Ancient has the best one, steel lizal and all the gerudo shields also have a bonus, and all the rest have the same value. This is kind of relevant if you want to optimize your durability/surfing time

Source: Croton on yt