as by subject. Especially in a colder place, where one would be wearing some sort of closed shoe or boot (say, Lapland), how would someone wade a 30 or 40cm deep river/creek without flooding one's boots? In theory one could suck it up and hope for the boot/shoe to get dry, but that might take a long time, and at near 0C temps, it might be pretty unpleasant.
You really don't want to be getting your walking boots wet under such circumstances, nor do you want your socks wet. So rather than going barefoot, swap to some more suitable footware for the crossing.
The best bet is to take some lightweight "water shoes" also sometimes known as "swim shoes" they're the sort of thing wild swimmers wear when out in unknown waters. Lightweight, quick drying, no good for walking long distances but usually designed to have good grip on wet surfaces.
And a towel, always know where your towel is.
If going barefoot is not an option, then basically 2 are left
Waders. Preferred by fishers standing in water up to waist. Heavy, take a lot of place, and keep in mind, you will sweat inside.
Sandals or running trail shoes. Take little place, light, choose one with good soles that will provide a good grip. Prepare for short cold shock and warming up your feet afterwards. It's still better than walking hours in wet trekking shoes.
and at near 0C temps, it might be pretty unpleasant
In fact it's only unpleasant for the first few seconds. Your feet warm up the water very quickly, and from then the boot acts like a wetsuit. I honestly can't think of many days I've been hillwalking in the UK and come back with my feet dry. In summer maybe, but not often between October and April.
The major problem with damp feet isn't cold, it's chafing. Cotton socks are usually a bad idea for hiking. Better quality materials (most notably wool; Smartwool socks are highly recommended!) stay comfortable even when they're wet.
If you're on a longer hike over several days, do pack several pairs of socks, and take every opportunity when you camp to hang up the wet pairs to dry. As good as Smartwool socks are, no-one likes the "slipping your foot into a dead fish" feeling of putting on wet socks.
The other issue which no-one's touched on is boots. If your boots are Gore-Tex, then they'll stay waterproof even when they get wet. If your boots are leather though, the wax gets washed away and then the "wetsuit" effect stops working. Use aqueous Nikwax (or whatever they're calling it these days) to reproof your boots every 2 days if they're constantly wet.
If you're caught out without alternatives, this is what I've done at very slightly warmer temperatures. If you can plan in advance, other answers provide better options.
Take off boots and socks, put boots back on to cross. Keep your leg-wear dry. Zip-off hiking trousers have their use even in the cold, or roll the legs up.
After crossing, do what you can to dry first your feet and then inside your boots. Perhaps you've got dirty or slightly damp clothes in your pack, for example. Any scrap paper can be used to get a bit more out of boots, while tissues aren't worth using on boots, only feet. Pack towels will often get out quite a bit, then wring them out, then some more. With some of my quick-drying gear, using the zipped-off legs to dry out the boots, then zipping them back on to dry as I hike would be a good option.
Then put socks back on, and boots, and get going. You might want to wear plastic bags over your (inner) socks if it's cold or your boots are very absorbent. Even small flimsy ones will help, though they'd leak if you wore them over your boots for the crossing. I normally have a few in my hygiene kit, for example.
Another good option that no one has mentioned so far: Gore-Tex® (or any waterproof) socks. If the trail is really wet, sometimes taking boots off before each stream is not feasible. I've worn waterproof socks in the past, and just let my boots get wet. Waterproof socks are surprisingly effective at keeping your feet warm and dry.