I've only lived in the East of Norway (So Oslo and close to Gardermoen Airport (Oslo Airport)) and the climate varies fairly drastically depending on where you live in Norway, for example if you live on the West coast (Stavanger etc) it will rain a lot more than in the East.
Here the temperature has drastic changes over the year. It is very common that temperatures will be -20C (at least!) in Winter and it can easily be over 30C in Summer (I've seen my outside Thermometer reach above 40C in the sun). Due to that there are two sets of tires required by law here, if you don't change from Winter to Summer tires you can be fined. During winter you can still have weeks at a time of perfectly blue sky, so don't get me wrong, it's not all bad! But most people do get tired of the snow and can't wait for it to warm up.
Snow can stay permanently on the ground from Mid October to May (that's the extreme range, usually maybe Mid November until March), and I don't mean a few CMs of snow, I'm talking one day there may be no snow and the next you wake up with 30cm (again this varies GREATLY depending on where you live in Norway, West Norway basically doesn't have much snow, and it doesn't stay long).
Because Norway is at such a 'high' Latitude (Closer to the North Pole) than many countries people may not be used to the amount of daylight which varies throughout the year. There can be days during summer where it simply never gets properly dark at all. This also means during Winter there are times (months) where there is only sunlight between maybe 9-4. The further North you go (Norway is a VERY long country) the less daylight you get during winter, there are places i Norway that have zero daylight during winter, none at all.
This lack of daylight can lead to people being more depressed at times. Lets face it, waking up and going to work whilst it's still dark, leaving work at 4 and it's already dark and all of a sudden you're never seeing sunlight during the week. That can be tough at times. However, the summer is beautiful, we can have months where there is almost idyllic (pefect) weather, sun all day with lovely blue sky and long days.
Due to the lack of daylight in Winter quite a few people take a short vacation to 'Syden' meaning France/Spain/Italy etc to get some sun and a break from the snow and cold.
Pros:
Great weather during summer
Mostly 20C+ and sunshine
Long days
Winter days with crisp blue sky is simply gorgeous
Cons:
Can be cold for months at a time (November-March 0C to -25C)
Sometimes it's much milder than that, but always on the cold side
Very short days in Winter, so little sunlight for long periods (depends where you live though)
LOTS of snow (depending where you live)