As I'm sure you know, that is the absolute darkest time of year (solstice on 21st or 22nd). It can be sort of fun for a holiday to experience that even if it's hard to live with for weeks on end, but it limits what you can do and how much you can see. Bad weather is also not unlikely to cause problems with accessibility and cancellations. Storms are common in December. A storm in Iceland is considered to be when the wind reaches about 45mph and there are many, many storms each winter. Even when it is not technically a storm, 30+ mph winds are standard (not every day of course!).
Having said that, it can be cosy in town and the lights are pretty and I agree the pools are very cool when it is snowing. There are some unique Icelandic Christmas traditions that are fun to learn about and you can see the Christmas cat downtown.
Although we had a very snowy Christmas last year, a white Christmas is actually far from guaranteed in ReykjavÃk as it often doesn't snow until January. No snow is better for travelling, but snow is pretty, so I suppose it's swings and roundabouts.
There are just fewer things that you can do and fewer places you can get to in the dead of winter, even in the best circumstances. In the summer you can hike into the mountains, get into the highlands, go further and see more, access the more remote jewels of the country beyond the golden circle. There's so much more!
All in all, if you want a short break mainly sticking to the city then I think Christmas time is OK if you're prepared for what it will be like (dark, cold, windy). If you want to get out and see the country, it's honestly not ideal and it limits your options considerably. But if it does snow, it's very beautiful. And of course you can always come back again another time to get out into the wild landscape properly.