There's some discussion of that here.
Some answers quote references, which point out that the Buddha allowed footwear in the wilderness and take that as permission to adapt to the terrain.
One says that some monks simply don't go outside at all.
One says that the strict interpretation of the Vinaya can't easily be adapted to a hostile climate.
One says that monks wear warm layers underneath and monks robes as the outer later.
I too have seen photos of a monk wearing snowshoes, and of monks wearing winter coats.
If for example you search for the word "footwear" in this
Modernization? The Great Standards
More than two and a half thousand years have passed since the Vinaya rules were originally set down by the Buddha, and many things have markedly changed since then. Should the rules be modernized and brought up to date? How can this be done?
Already during His lifetime, the Buddha made special allowances for different regions (or desa) outside the 'Middle Country' of North India — where He lived and taught. These dealt with both the workings of the Community — for example, a smaller quorum for ordination is allowed in distant parts where there are fewer monks — and practical measures, such as special dispensation for footwear and bathing. So there is a precedent for adapting to conditions, but this does not mean the abolishing of any rules.
The Lord Buddha also left us a set of principles that can still be used as a standard to judge new circumstances. These are known as 'The Great Standards.' Properly used they should protect against a wholesale dilution of the Rule.
The next section warns against blaming others, by the way.
There is always an exception in the Sekhiya Training Rules for "one who is ill" so that a bhikkhu may, for example, cover his head when the weather is unbearably cold or the sun dangerously hot. The same applies to footwear, which normally should not be worn in inhabited areas.
... with this footnote ...
The Buddha did make a special allowance about footwear for 'outlying border regions.' In some western countries going barefooted would not be socially acceptable and might even be against the local bye-laws. The Great Standards should be used to decide what is suitable.