Just checking in to say that as a kid, when I heard about the Bering land bridge during the last Ice Age and how it allowed humans to populate the western hemisphere, I imagined a flat roadway about forty feet wide with Mongol parents trudging along, holding their kids’ hands as they walked.
I’d rather my 4x4 had a wench.
Have you seen what building a rail line over northern lands is like? it’s worse than a road. The recently in the news rail link to Churchill on Hudson’s Bay is apparently limited to a 30mph speed at best thanks to permafrost. I went to a talk on mineral resources in Siberia where it was mentioned that one town (the location of the Gulag in One Day in the Life of Ivan Dennysovich, I think) every spring they move the dock equipment half a mile back from the river for the spring thaw.
But yes, I don’t see an open road as an option specifically because even if properly constructed, it requires a week of driving to get somewhere, through basically deserted terrain. Even conventional trains wouldn’t be terribly relevant, given the maintenance costs and the fact that there is not a significant speed advantage over Pacific shipping. High-speed rail (say 100mph minimum) would mean a shipping time of 3 days give or take, from China to USA. However, until the transiberian is upgraded to the same level, no improvement for European connections.
More likely is - watch for full upgrade of rail links from China via south Silk Road routes to Europe first.
it will be a long time coming…
Obligatory mention of The Gods Must Be Crazy where both winch and wench figure in the plot.
The big problem is that we already have a link that supports an enormous amount of cargo already. Container shipping across the pacific is already cheaper per ton mile than rail shipping across the US.
To answer the OP directly, no.
The first problem is… you can’t drive to Nunavut. Even the Top Gear expedition, cited by Colibri started at Resolute, NU and they didn’t drive there.
You’d be headed the wrong direction anyway.
That said, you COULD drive up through Alaska to Deadhorse,AK then up to Prudhoe Bay and follow the shore towards a point near Barrow (Utqiagvik), AK. Then you would need to head out over the sea ice, skirting the Chukchi Sea landing in Siberia somewhere near/past Wrangel Island.
After that, you’re on your own though, as there are only isolated and abandoned settlements that are only accessed by water or air. There are no roads, rail lines, etc… for thousands of miles.
If the basic idea of the OP is to attempt a land based mode of travel over polar ice in the winter to cross from North America to Russia (ignoring the specific route suggested, and the assumption that the ice could consistently bear the weight of a 4x4 truck, or that the snow cover would be “packed and relatively flat”, all of which are dubious assumptions)…
And leaving aside the fact that, with the accelerating global warming of the past 50 years or so leaving us with less and less polar ice, such that a Northwest Passage through the Arctic may not only finally be possible but persist year-round…
It has, in fact, been done by skiers in 1988, albeit in the reverse direction of travel, in The Soviet–Canadian 1988 Polar Bridge Expedition, which took about 3 months to do, as it “began on March 3, 1988, when a group of thirteen Russian and Canadian skiers set out from Siberia, in an attempt to ski to Canada over the North Pole. The nine Russians and four Canadians reached the pole on 25 April and concluded their trek on Wednesday, June 1, 1988, when they reached Ward Hunt Island, Ellesmere, Northern Canada.”
It’s apparently also been done by vehicle, as I posted somewhere upthread (and which everyone has seemingly ignored):
Here’s another cite, with pictures:
Yes, it can be done, but if I had to try, I would start in Florida, take a modern version of this, and head for Murmansk with the help of the Gulf Stream and pray for the best.
BTW: Last time I was in Irkutsk by the Baikal Sea (that was in 2001) most cars had the steering on the right, because they were half-illegally imported from Japan via Vladivostok, or so I was told by the locals. There was no road to the West (Moscow, also known as the “main land”), so there was also no need to adhere to the road regulations there. OTH I saw a shrine to some poor dead Siberian every couple of hundred meters on the way to the Baikal Sea on a perfectly straight road. I don’t know if people crashed in winter, when the conditions would be horrible or simply did not know on which side of the road to drive. Many, no doubt, were also very drunk.
That’s insane!! They brought three months worth of diesel fuel for what was essentially a floating bus?
And also benefited from Divine Intervention!
Passing on the bumper hitch mounted crapper from his first movement to the magnetic pole?
Sarah Palin would be the person to talk to, IMO. She was governor of Alaska, she can see Russia from the state she governed, and she has experience in building bridges to nowhere. 
Irkutsk isn’t nowhere; it’s the Paris of Siberia, don’t you know.
I think that’s what Andre Agassi said when he decided to go “four wheeling” with a military grade Hummer outside of Las Vegas through an area that some of the locals called ‘the bad lands’.
One day and several tow trucks later, what was left of that military grade Hummer was towed into the lot of the dealership it came from.
Funnily enough, the following newly made video popped up in my RSS feed today: Why no one is going to build a bridge between Alaska and Russia