Winter activities in Copenhagen

I am a mid 50's woman, travelling to Copenhagen in February, to meet my daughter who is studying there. I have booked an Airbnb in Christianhavn so accommodation is sorted. I am there for 5 full days.

I would appreciate some advice on what activities are best for this time of the year. Obviously it will be cold. I like to bike, kayak, walk and horse ride, but am not sure how much I will be able to do in the weather. I do like museums and history, so will obviously try and do some of those. Is there ice skating available or winter (horse) riding anywhere?

Is it worth making an overnight trip to Louisiana/Helsingor, or just do it in a day trip>

Also some affordable restaurants, any sort of ethnicity is good. Daughter says food is very expensive and eating out is beyond her student budget most of the time, so would like to take her out most nights I am there.