As of URW version 3.30 the ice can break now.
Lakes start to freeze when the weather gets cold enough. This doesn't happen the same time every year, and the ice also doesn't grow equally thick every year. And when the lakes freeze, they now freeze gradually.
The ice cover first starts to build up at shallow water and proceeds towards deeper sections from there on. How fast the ice cover increases or decreases depends solely on the weather. Ice thickness can also vary at different sections of the lake. It's not anymore safe to walk on the ice as soon as there's ice cover on the lake. Thin ice can break under any load it can't hold - be it your character, NPCs, animals or items.
There's a confirmation to step on the ice if the character doubts the ice will hold. This applies to thin ice which characters can easily recognize by stomping on it to see if it cracks. Notice that even if there are no doubts and confirmations the ice still isn't necessarily safe to walk on.
It's not possible to travel on the ice on world map when the character doesn't trust the ice completely.
If that's the case a message to zoom in to travel on the ice will be shown. This way the character can't mistakenly step on unreliable ice on world map. However, it should be noted that the ice can't never be trusted completely and even when you are allowed to travel on the ice on world map it can still break. Should this happen, the character is forced on zoomed in map where he/she needs to navigate to safe location.
Falling through the ice .
If you happen to fall through the ice climbing and pulling yourself back onto the ice is not easy and depends on your climbing skill, agility and strength. All of these factors are tested on each turn you try to move from the water onto the ice. Wielding any sharp pointy weapon such as knife, sword, spear or even an arrow will improve your chances to pull yourself out of the water. Swimming skill is also important as it determines for how long and how easily you can keep struggling in the water.
If you're unable to get out of the water after 5-10 minutes, you're almost certainly not going to get out. Your body temperature starts to drop as soon as you fall in the freezing water, and when hypothermia sets in you will eventually lose consciousness and drown. Depending on your swimming and climbing skills you will also build up certain amount fatigue on every turn you spend struggling in the water, and the more fatigued you get the lower your chances to pull yourself out become.