If you are doing lots of road miles, new over remould are nicer as a rule. But tbh, remoulds are fine to their rated speeds, same as anything else. And you'll often get more aggressive treads in remoulds.
But it will be a trade off, the better the tyres are off road, generally the worse they will be on road.
If you are looking at new tyres, I'd say look for MT's with sipes in, these will likely be better in the wet and snow than ones without.
Maxxis is offer some nice tyres, the Bighorns MT764 and 762. I also like the Trepadors if you want a directional tyre.
I also like the look of the Federal Courgia MT's.
And I'd also say look at the Copper STT Pro and the new General Grabber MT. All look like they should be nice multi purpose MT tyres.
If you fancy a remould, then I'd recommend the Yeolander MT copies. Such as the Fedmia Extreme, although most remould makers sell a variant of this, so just have a look about.
It's super capable off road, but rides on the road far better than it should given it's off road credentials. However in the wet or ice it won't perform as well as the new tyres I mentioned above when used on tarmac, mostly because it has no sipes.
As for size, well tbh you only really need to keep it to a similar diameter you have now, you don't have to stick with that exact size. You can probably go +- inch on height too with no negative affects, although I probably wouldn't go shorter.
As a rule in the UK narrower tyres tend to work better in the mud than wide ones. Plenty of tyre calcs online to help you figure out what profiles you'd need for what widths.
As a side note, D2's rely on TCS to make all 4 wheels spin. Is your TCS working? Also to make the TCS work, you need to keep on the throttle a little bit. You need the wheel speed for it to work. Lastly, some years of D2 have a centre diff lock on the transfer box, but no linkage. It would be well worth retro fitting a linkage to make use of the diff lock. That way the TCS won't have to work quite so hard. All this should help maximise traction on slippery conditions, regardless of tyres.