Probably. Fair warning: I’m going to be guessing here, and thinking through it, so I could be missing something important, or just flat out wrong.
Normal full plate isn’t just a slab of metal between you and the outside world, if it was it wouldn’t be very effective against blunt weapons; like maces, flails, mauls, warhammers, and morningstars.
Those were all weapons designed to transfer a lot of kinetic force through plate or chain armor, breaking the recipient. Plate works fantastically against swords, some axes, and polearms in certain circumstances, but, ultimately, if you’re a giant bell and someone else has a hammer, I can completely botch a metaphor.
The solution was to wear a layer of heavy padding underneath the plate. This would be flax or any other easily available fabric, that could then provide some kinetic protection, in addition to the plate’s protection from weapons like axes and swords.
Okay, so that’s the part I can say with confidence, here’s the part where I’m guessing.
The padding would probably provide some insulation against cold weather on it’s own. By design it’s basically just a thick coat under the plate anyway. If that’s sufficient to keep a soldier warm enough to fight, then that’s all it takes.
But, if it’s not, then you’d need to supplement the padding with something that would keep your combatants warm, and furs are an obvious choice. Now, I don’t know that furs would actually absorb as much kinetic force as the padded armor, and you can’t just add extra stuff under the armor without heavily reworking the plate. So you’d probably need to either sacrifice some of the padding for more warmth.
Depending on how the plate is articulated this might not actually be an issue. If you can slap a fur cloak over the armor, or even just attach fur over the plate itself, you might be able to keep your soldier warm when they’re not fighting without substantially increasing the weight they’re carrying and without accidentally freezing them.
I’m kind of preferential to the cloak because it’s slightly more likely to survive combat, and this gets to another issue. During combat, the issue wouldn’t be keeping your soldiers warm, it would be keeping them from overheating.
Anyone who’s ever worked strenuously in a cold climate should be familiar with this phenomena, but, while you’re engaged in heavy physical activity, including combat, you’re body will generate enough heat to compensate for the environment. You’ll feel the cold, but it won’t impair you. This can create a weird situation where while being active, you’ll actually feel too hot in your snow gear. You’ll perspire into it, and then you’ll end up with it drenched when you stop working. If you’re wet, your body temperature is dropping, and if your environment is cold enough, this can spiral into hypothermia.
For someone experiencing this today, the easiest solution is to wear layers, and toss off outer layers while working, so they remain dry, preventing excessive perspiration, and then put them back on when you’ve finished. But when you’re wearing full plate and in combat, that’s not an option.
In the case of your soldiers, this can create a situation where they’d actually sweat into their gear and face more of a threat from the cold after combat, assuming they had no place to make camp, and warm up.
It’s probably also worth pointing out that winter campaigns in northern climates have been a very bad idea through most of human history.
I hope this is useful, even if it is a little more speculative than I’d like.