The closest airports, Alert, Eureka and Thule are run by the military. They do not welcome tourists.
The closest civil airport seems to be Resolute. Twotters from there have been known to do flights to the pole; sometimes even land nearby to pick up people who have taken it in their heads to hike/ski/swim there.
March is a good month for this as there is daylight and ice to land upon.
Perhaps Ken Borek Air at Resolute may be hired to position some fuel drums at a farther North landing strip that your tires would be suitable for -- they use tundra tires.