February travel to Shirakawa-go, Takayama

Not the first time in Japan and the places above, but I came from a summer through out country. This will be my first time in a snow winter so I'm worried with a few questions.
1) Will be landing in Nagoya and stays there first night. As I'm not sure the quality for winter wear in my country, so I decided to wear thicker and purchase in Nagoya. No ideas about winter wear, looking just by a set as only chance to wear is traveling to winter country. Can I just buy ski wear and snow boots as thinking of going to try skidding. Will it be strange to wear ski wear in city.
2) will be traveling by 3 days bus pass to Takayama area, will there be transportation problems, and any public transport to nearest ski resort in Takayama.
3) As in winter, my knowledge is only lip balm, any others protection needs to repair too?

lip balm is not for winter but for countries with low humidity. moisturise for skin is needed to.
usually buses and trains will stop operating if there is snow road closure. if you can board the bus or train there should be no problems. the best is still taxis though.

Can I just buy ski wear and snow boots as thinking of going to try skidding. Will it be strange to wear ski wear in city.

Sure, but you may better off visiting a Uniqlo when you arrive and getting some warm clothes for travel (pants/jacket) as it would be more comfortable everyday than ski specific wear. You can rent ski wear at the mountain.