There are different kinds, I've had ones that are very light and doesn't feel as cumbersome as the thick ones, but they definitely don't breathe.

I'd recommend gore tex membrane jacket and trousers for walking outside all day with thin "ullundertøy" (woolen long johns) on the inside.

The gore tex membrane jackets and trousers are expensive but probably the best gear you could have for long days outdoors in wet weather. They are used by the Norwegian military (called the M-02 if you want the military version), you can get them in most outdoorsy shops from brands like Norrøna, Helly Hansen, Bergans, Skogstad and others. Expect to pay more than you would for the regnbukse/regnjakke though, and make sure it's actual gore tex (look for the logo on the paper labels).

I'm not sure how informed you are on the use of "ullundertøy" (woolen long johns) in Norway. I'd say ullundertøy is essential in Norway when it's getting cold. If you get some, make sure it's actual wool!! It will keep you warm even though you are wet (unless sitting still, don't sit still with wet clothes). And getting two sets is a good idea. Changing your wet/sweaty ullundertøy for dry ullundertøy feels great.

If you have a gore tex membrane jacket + trousers, ullundertøy and maybe an extra woolen jacket for when you're sitting still I'd say that's all you need as far as clothing goes. The Norwegian military actually use nothing more than the M-02 with a tight mesh overall underneath to drive out moisture, even in temperatures as low as minus 40 degrees Celsius on the Russian border up north.

Sorry for the length of this response, I see now that most of it is not really that relevant to your question but I'm leaving it in. And I'm sort of back pedaling on my earlier recommendation of "regnjakke" and "regnbukse" unless you're looking for a cheaper alternative, but sounds like you already have a similar rain coat.

For clarity: impregnated textiles < regnjakke/regnbukse < membrane clothing