[McKay (OP)]

Even a double pane window, if I put my hand to it, I can feel it is very much colder then every other part of the outer wall and the rim of the window (in a cold climate, ofc), though glass is a poor conductor of heat.
Is it only because of how thin the glass piece is? If I would have a window glass as thick as my outer walls, would the insulation be as good (or even better than) .. the wall itself?

[yor_on]

That should depend on density, and how good it reflect and isolate that heat, wouldn't it? A vacuum between the windowpanes use convective heating/cooling, as in there being no matter able to kinetically interact, transferring this heat (or lack of heat) from one side to the other. Something silvery uses radiative heating/cooling, meaning radiation (as 'photons') being reflected. And then you have diffusion, as you leaving your hand in constant contact with that window. I don't know to what degree a solid wall of glass leads heat? Neither what wall you compare it too.

[PmbPhy]

Even a double pane window, if I put my hand to it, I can feel it is very much colder then every other part of the outer wall and the rim of the window (in a cold climate, ofc), though glass is a poor conductor of heat.
Is it only because of how thin the glass piece is?

Yes.

If I would have a window glass as thick as my outer walls, would the insulation be as good (or even better than) .. the wall itself?

Yes.

[alancalverd]

Glass is a better conductor than air, which is why double-glazed windows, whether filled with air, nitrogen or argon, insulate better than thick glass.

If the walls of your house are properly constructed, they contain a lot of air, at least as a cavity between brick layers and more often in a foam or wool to prevent convection. Bricks and breeze blocks have marginally lower conductivity than glass and a plasterboard (sheetrock) liner is a fairly efficient insulator, especially if spaced 2 cm from the brickwork on battens (thus trapping more air). So I regret that in all practical cases, PmbPhy's second answer is wrong.