You haven't given many details, but let's assume that since you're stated the flight path leads to the arctic circle that Barrow Alaska would give us a rough idea of your end-point. LAX (you stataed that you're currently in California) to Barrow is 2548.5 Nm. You've suggested a 2-seat seaplane. Lets use a Citabria as a possible seaplane for the mission. A Citabria on floats will cruise at (maybe) 100mph (86 kts). To fly from LAX to Barrow in that plane would take 29.6 hours. Use $200/hr as a rough estimate of the cost of the plane and pilot. You're already at $6,000 (each way). 29.6 hours is too much to fly straight. Let's assume your pilot is good for flying 8-hours per day. That's 4 days flying, each direction. Where are you sleeping at night? Tents, Motels, the Aircraft, etc? If it's tents, you're not going to be flying that little Citabria mentioned above. The Citabria I did my seaplane rating in would have been at or over gross with two (skinny) pilots in on board and full fuel in the summer, nevermind with winter jackets, blankets, and wilderness suppliers. So let's assume you decide to try this in a more realistic plane. A C-172 on floats. Similar cruise speed, but now you're probably $250-$300/hr. You're now looking at $9000 (each way, $18,000 round trip) for the plane and pilot, but you have an IFR capable machine that may be able to carry enough baggage. You still have the issue of where you're going to refuel. If icing is an issue in that area at that time of year you may want a plane certified for flight into known icing. Now we're talking much larger and more expensive aircraft that probably isn't on floats. How long are you going to stay by the arctic circle? Are the plane and pilot just going to wait for you, or are they going to drop you off and come pick you up days/weeks/months later? That just doubled your cost or you're going to be paying for the downtime the the plane & pilot aren't flying when they're with you in the middle of nowhere.
But rather than talking to a bunch of people here on a forum that may (like me) have no experience in this kind of adventure, you should really call up a few operations in Canada/Alaska and get their input. They would likely be able to point you in the right direction and give you more details you'll need to consider before the trip.
Or you can fly from Fresno to Barrow commercially (round trip) for $650 via Alaska Airlines vs the around $20,000 in a light-plane.
