At any rate I strongly advise you and anyone interested in a trip to Iceland to avoid the entire 3 months of November, December and January. Unless you really want to see NYE or something, but really why would you, there are fireworks and bonfires in other places. The snow, ice and northern lights are very lovely but snow also makes travel more tricky, slippery pavements aren't fun, and there are no guarantees about northern lights anyway. When it isn't snowy (usually doesn't snow until December or January) it is grey and dark and depressing.
February, March and April are OK with the daylight coming back but are usually snowy, sleety, windy, soggy, puddly sort of months and the interior of the country is still closed. It's all right but early winter before the snow is always nicer than late winter when the snow melts and everything is brown (Icelandic winter lasts at least until mid April, do not think that this period will be spring like in any way).
May, June, July and August - absolutely lovely. Of course there is still bad weather and it can be windy and rainy but this is Iceland at its best. As the summer arrives in earnest you can start accessing the jewels of the highlands. The light is exhilarating, the birdlife is amazing. As the darkness returns in August you can see the first northern lights of the season.
September and October are often very nice indeed. Autumn is short but beautiful. It can be very stormy. The highlands are usually still accessible in September.