Frostbite is a status effect in Remnant: From the Ashes. Like other status effects, it has a bar that will build up the more you are exposed to things that cause the status. These can range from strange frozen plants that will explode in a shower of ice to different types of attacks from certain monsters, like the large Yeti-like creatures introduced in the Subject 2923 campaign.
If you let it build up too much, ice will form all over your body, and you become Frozen. Thankfully, this doesn’t freeze you in place, which would be a death sentence, but it will severely slow your character, which might as well be.
Frostbite buildup will diminish once you stop taking damage from sources that cause it, but if you want to hurry the process along, you can find a nice fire and stand beside it. Most of the frozen areas will have campfires and bonfires dotted around the area, allowing you some respite from the bitter cold. Hanging out near them for a while will reduce the Frostbite level and help you get rid of the Frozen effect quickly.
Once you get Frostbite to the point of becoming Frozen, you will need to wait for the indicator bar on the screen to go all the way to the bottom before the effects of being Frozen wear off, but it is still beneficial to be near a bonfire or campfire to speed up this process.