Road trip to Tromsø (polar circle) in late May: what tires?

I’ve got my eye on a new epic adventure: driving up to Tromsø to see the midnight sun. I will probably start in Netherlands.
In my home country Netherlands, the weather is very pleasant in May. In fact, the weather is alright year round. I don’t even own winter tires for my car. That is a big contrast with Norway, especially north-Norway. I needed snow chains on my last trip there. That was in winter though. Winter tires aren’t useful over normal tires above 7 degrees, but they do work well in snowy conditions.
How are the roads to Tromsø in late May? Will summer tires be sufficient? Will I need to swap tires halfway the trip? If so, how do I judge where? Would all seasons be a better idea?
Please note: Yes, flying would be easier, but it wouldn’t be a road trip if I took the plane, right?
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Drive to Tromsø | Norway | Road E8
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Images: Erik Mclean, Daniel Torobekov, Erik Mclean, Erik Mclean