Figure Out What Tone You Want
Thomas Markov's answer correctly identifies that the DMG and specifically Rime of the Icemaiden included rules for this.
I am at the tail end of running that campaign, and I can unequivocally say that those rules suck.
At no point was hypothermia an interesting part of the game. Everyone got the idea (correctly) early on that cold was dangerous, and took steps to avoid it. Mostly by finding ways to get cold resistance. At that point, that aspect of the game went from tedious to irrelevant. Hooray?
What’s worse from the GM side is that one player didn’t have resistance. So, the whole party would have had to care about the Stay Warm! minigame (which they despised), if I hadn’t quietly stopped enforcing it. Even if I had decided to continue, it would have been equivalent to just punishing one player, over and over again.
Bottom line, those rules have only two modes: tedious or irrelevant. So you should absolutely not use them. If the next release has detailed rules for bowel movements, you should avoid using those too, for exactly the same reasons.
Instead, think about the tone of your game and what parts your players find enjoyable. If this is a gritty game and they enjoy role playing the desperate struggle for survival, your Goliath should be huddling around a fire regardless of mechanics. If they enjoy heroics and fighting, you can gloss over the aftermath (whether or not he feels cold or sits around the fire is a bit of background detail, not a real plot element). If they like physical comedy, do whatever seems funniest. Etc.