According to the Danish Rent Act, it is as a rule the landlord who is responsible for removing snow and the tenant is paying the expenses for this through their rent.
As a tenant, you can in agreement with the landlord get specified in your lease contract though that you yourself take care of the snow removal, and therefore will be entitled to a reduction in rent.

If someone slips and gets seriously injured where the snow is not cleared properly, a possible claim is always retained by the owner or landowner. Tenants are not liable even if they have taken responsibility for clearing snow.

Pavements, stairs, etc. must be cleared of snow shortly after the snow has fallen. The responsibility includes the first ten meters from the property boundary.
Basically, the pavement in front of your property needs to be free of snow from seven o’clock in the morning until ten in the evening.
On Sundays the snow must me cleared from eight o’clock in the morning.

Read more at:
Danish Property Control Act
Danish Rent Act
Also check your municipality's website for regulations regarding winter maintenance.