Buses may be easier with bags
Mother and I stayed at Cabinn City when we arrived from LAX-LHR-CPH at 5 pm, and we used Bus 5A from the airport to a stop merely a 200-m walk to the hotel. It took longer, but there were three advantages: (1) Seeing things from the bus and (2) little vertical level changes dragging our bags.
And (3) was the risk of being approached by undesirable figures outside Copenhagen Central Station while walking to hotel. (They don't approach you when walking TO the station or when carrying only your day bag.)
Using the Metro will guarantee a bit of vertical travel, often being a struggle between taking your bag quickly up a few steps and walking/dragging a long way to an elevator. Using the train may or may not be somewhat better.
So do check out the bus lines that depart from the airport station!