Let's start with what the DMG has:

EXTREME COLD:
Whenever the temperature is at or below 0 degrees Fahrenheit, a creature exposed to the cold must succeed on a DC 10 Constitution saving throw at the end of each hour or gain one level of exhaustion. Creatures with resistance or immunity to cold damage automatically succeed on the saving throw, as do creatures wearing cold weather gear (thick coats, gloves, and the like) and creatures naturally adapted to cold climates.


Magic for cold weather doesn't seem to exist, just for Cold attacks. Still, if you can afford or acquire that, you're good to go.
This message was last edited by the GM at 04:06, Sun 21 Oct 2018.

The Setting thread for this game has a look at clothing options, but the short version is:

Any quilted/padded armor will be equivalent to thick clothing, but will need better gloves and boot, most likely.

Locally acquired Quilted/Padded and Hide Armor is made with the winters in mind, and count as thick clothing including gloves and boots.

Hats may be an issue, and cloaks to keep the rain off are not included.

Robes can be worn over most armor and clothing, and will turn traveler's clothes into basic cold weather clothing. They may help offset the heat dissipating properties of metal armor in the snow, but not by a lot (unless enchanted, of course). Keep in mind that robes are only an extra 4 pound of cloth, presumably wool. That's why they only help over Traveler's Clothing, which is already built for milder chills. It's still not as good as Furs or heavy quilted clothing. It will provide only partial protection vs the full effects of extreme cold.

There is a minor magical item produced at The Keep in Siberia if you can afford it that protects one down to -20 degrees even in metal armor. In keeping with the rules regarding magic item creation in Xanathar's, you'll need to acquire a rare component to make it from. That will be covered in The Keep thread. It should be fairly affordable. More or less.
This message was last edited by the GM at 02:23, Wed 01 Jan 2020.

The DMG doesn't have much on Cold or any other extreme environment, really. Enough to visit, but not for living there. So I'm going to fake it. So...a House Rule:

Thick winter clothing is not compatible with metal armor. You can wear padding under it, but not winter clothing, and not enough padding to keep you warm in spite of the cold metal.

All medium and heavy armor, other than Hide,is just a big dangerous cooling fin helping leach the heat out of your body. Unless you have magic, of course. Consider it to give Disadvantage for any extreme cold weather saves. Robes worn over the armor will negate Disadvantage, assuming you can actually keep them closed. and the heat in. It may not always be possible.

You have been warned.
This message was last edited by the GM at 21:49, Sun 04 Nov 2018.