Where can I go for budget holidays in January?

I am turning 30 this January and would like to spend it some place special.
Original idea was an ice hotel in Sweden, but I can't afford it right now and so looking for alternative.

I don't think I want any sun destination. I would rather go for some adventure or city break somewhere in Europe.
I don't do any winter sports and don't have any truly winter clothes and to buy them probably is too expensive. I live in Belgium and will be going on that birthday holiday with my boyfriend.

Any help will be appreciated.

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