Firstly, most all terrain tyres are pretty poor in very cold conditions because they don't have enough sipes or soft enough rubber. They might be alright in deep snow but would suck on ice. Most people up here don't use "european" winter tyres but nordic ones, which have an even softer compound, more sipes and even some special gritty stuff in the rubber. The standard european winter tyres are designed more for going through warmer heavier slushy snow, whereas the nordic ones work better on ice. Studded tyres of course work the best on ice but there is no way you would want to drive all that way from the UK on them even if it were legal. They have a lower speed limit too.
I did my first winter here on Nokian hakkapaliita CR3 which are the nordic non studded tyres, they were loads better than normal winter tyres I'd used in the alps, even on roads that I had trouble walking on without falling over. I'd also driven them back to the UK and they handled alright in warmer wet conditions and the wear was good too. You definitely notice them squirm in the corners though when it gets warmer. If there is a one tyre does it all option for this trip, that is it. Normal all season tyres will be no good in the winter up north, the norwegian garages only sell them as summer tyres.
Unfortunately though I still had a crash with those CR3s on, going along a perfectly straight road at 40 mph, and a slight change in camber sent me off sideways. Luckily there was no one coming the other way and the damage was minor, but I'm not taking my chances again so it's studs for me from now on. Generally the roads are really well cleared and gritted here, but the one time that they aren't, or a giant moose walks out in front of you (happens quite a lot) and a swift end to your road trip could be the least of your worries.
I live in Oslo and would be happy to store some wheels for you if you wanted to swap over en route to studs, otherwise pretty much all garages here have a tyre hotel where you can pay to store your wheels. You would normally be fine driving up to norway on decent commercial tyres with plenty of tread, but bear in mind that soon you can be fined in germany for not having at least all season tyres with the 3 peak snowflake sign on them in the conditions are "wintery". There are normally plenty of part worn studded wheel sets going on Norway's equivalent of ebay, finn.no just search for vw t5 pigg. Give me a shout if you need help with that.
With regards to starting a cold temps, I've started a 2.5 T5 in -28 without a heater, I've heard people saying they have managed in -35 with a bit of effort. The main problems I've had in the past are with the diesel gelling in the alps, but up here the diesel is always good for down to at least -32 for the period that you would be here, regardless of where you buy it from. I also installed a oil sump silicon heater pad on that 2.5 using aluminium epoxy (make sure you insulate the other side with soldering mats or something or it will burn the sump cover) and it would start in those temps on the button, but you need somewhere to plug it in. My 2.0 t5.1 that replaced it comes with a webasto engine heater like most of the vans here, which is awesome, but probably a bit much for one trip!
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