You may visit North Cape mid-winter. As I did on February 19th 2012. Made I flight by Finnair to Ivalo and went by rental car to the northcape: around 450km. I did it with a cheap car, VW Golf 1.2 (Hertz: 80 euro a day, unlimited km). All rental cars in Northern Finland are equiped with spikes. It take around 6 hours driving time and you will pass a splendid landscape with terrific views. On my way to the North Cape I had a kind of snowstorm. On the way back I had splendid sunny weather.
The last part to the cape you will need to join a convoy. It leaves at 11.30 and 12.30 from Skarsvag. I stayed one night near the North Cape in a cheap cabin (www.northcapecabins.no, 450 NOK or around 50 euro).
You will have to pass Northcapetunnelen (2x 145 NOK) and Nortcape will cost you around 235 NOK.
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