A long time ago I wrote an article about weather and the kinds of effects it can have during a game. I now want to swing around and go over it more specifically. This time I'll be looking particularly at winter weather. If you go to the mountains you'll run into it, and chances are high that your current campaign has a few months of the year with snow.
What The Rules Say
The Dungeon Master's Guide says that in extreme cold you must make a save or gain exhaustion. In practice this is a simple rule that does a good job of penalizing characters for not properly being able to keep warm in reasonable weather, as well as force the players to recuperate to go back to normal. However, what if this cold is different? What if it's an ice plane far colder than what normal weather would provide? For that, you'll need some good old house rules.
So Cold It Hurts
A common approach to cold weather is to inflict damage on characters. A d6 seems to be the most common in these cases, and I find it's the most common dice to go to for minor damage in general. Maybe it's how common d6s are. More interestingly, the last campaign I played in that featured cold damage always had 1d6 of damage done. What changed as things got ever colder was how often the roll was made. Just bitterly cold, but still significantly colder than what the Dungeon Master's Guide says? Well, that'll be 1d6 of cold damage per hour. You got teleported to a plane of ice? Well, that will be 1d6 of cold damage per 5 minutes. You opened a hole to an even colder plane of ice? That might be the same as taking an ice breath to the face. You could of course do flat damage, and I seem to recall one situation from that campaign where we took a flat 1 cold damage.
Nice thing about this approach is that it can add a bit of a survival aspect, and helps to chip away at some of the health points of the characters, as well as their hit dice. Of course, this usually means less combat in favour of fighting the environment. It can also be rather niche, since that world was basically in a magically induced ice age.
Slowing You Down
Massive dumps of snow make it difficult to travel. Seems reasonable, right? However, it's often forgotten in the excitement of a game. I'd say we should pay attention to it though, especially for time critical tasks. Having these kinds of situations can force the party to more carefully consider their options. After all, if they are being chased it adds an extra factor. Perhaps the ranger has an idea to cause an avalanche behind them and slow down their goblin pursers? There are also possible complications from trying to make horses run through deep snow.
Food and Water
There's snow around so access to water is very easy. Unlike a desert or a forest, this makes it far easier to meet this need. However, food can be a different issue. In this way the last campaign I played this is exactly what happened. Water was easy, which was nice since it built levels of fatigue faster. Of course we had to melt it first. However, we often had to bring our food with us due to the higher DC for finding food, and we were without a ranger.
The other interesting thing about cold weather is that changes in either directions can cause issues or complications. A warm up while trying to cross a frozen river or lake can result in disaster. Likewise it can result in flooding making things further more difficult, especially if overflowing wizards take out bridges. And then having the weather go colder can cause issues as the above effects take over. Then you have the potential for blizzards causing massive snow build ups that could hide dangerous drops, and massively hurt visibility. This is one aspect you can have a lot of fun with.