Hopefully, you've already checked the weather forecast, but what will it actually feel like??
The weather in Copenhagen can be unpredictable sometimes, but generally speaking, here's what you can expect at different times of year:
January-February: It's cold. The temperature usually hovers around freezing. Bring your winter coat, scarf, and comfortable boots and sneakers for walking. It wouldn't hurt to pack a hat, gloves, and maybe even some base layers (wool or Uniqlo Heattech are my recs) if the forecast is looking particularly bleak.
March-April: You're still going to need a coat while you're here, although we're probably transitioning from heavy winter coats to slightly lighter coats (think quilted, wool, or trench coats instead of your giant puffer). We often get signs of spring this time of year, but it's not uncommon to get snow, too.
May-August: It's warming up and we're getting more sunny days. Most of the time, a light jacket or sweater will be enough during the day! Hopefully, you'll also be able to wear shorts, skirts, dresses, and sandals at this time of year. July and August are usually the warmest months, but we often get a lot of rain in July, too.
September-October: This is when we get our "autumn" weather. Think jeans, sweaters, and transitional jackets/coats. It's usually not that cold yet!
November-December: Winter coats have made their appearance. See also: January/February :)
No matter when you are coming, you will want:
comfortable sneakers for walking
a raincoat or water resistant winter coat
a tote bag or backpack to carry stuff around, since you will likely be out and about a lot!
Of course, check the forecast before you come, in case it says something wildly different than I've written here, but hopefully this helps!