Yes, in the winter period rental cars will have winter tyres. I imagine it would be illegal to rent out a car without, as it wouldn't be legally roadworthy.
The "one week after Easter" is a bit of a joke. Its based on the idea that half of Norway heads to the mountains for a last bout of ski and snow in Easter week and then the season is over for most people. This year I kept the studded tyres on for at least three weeks extra, risking a fine if caught, because we were heading up to Kvitfjell. As it turned out we had sleet and snow in the mountains, so I'm very glad I did.
Additionally its illegal to use summer tyres when conditions demand winter tyres, even outside of the winter period. So to be a law abiding citizen you might need to drive around with both sets of tyres and be prepared to change them as needed! Meanwhile, back in the real world, common sense prevails.