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I've heard from some site that is very cold there so if I want to have good experience with cold!!
Where is the best place to visit?

You should visit Santa in Rovaniemi, the Christmas Capital of the World.

On that beautiful moment in winter, Christmas light, you can enjoy snow with romantic twilight

This country is one of the northernmost areas in the world. Winter in Finland varies in duration from 3 - 7 months depending on the part of the country.

If u are outdoor type, you can go hiking in Lapland. With a plethora of national parks, strict nature reserves, vast tracts of wilderness and other recreation areas, Finnish Lapland is every hiker’s paradise. The sparsely populated region has fells, lakes, forests, rivers, ponds, bogs and groves of dwarf birch — everything that a hiker needs to enjoy the stillness of nature in a unique and pristine environment.

For renting skis, canoes and other equipment, you can contact skiing centres or customer service points in national parks. The customer service points of the Finnish Forest and Park Service also provide maps and expert advice.

I wouldn't recommend you to go skiing near Helsinki or the Lake district (I assume you meant eastern Finland) by new year, since it's not 100% sure that there will be snow. Or of course they have this fake snow that they shoot on the hills if there's no natural snow, but skiing on natural snow is much better than on fake.