Open the walls and add better insulation is the only cure.

nothing we can do as the renters?

I would think there is more than lack of insulation creating that much condensation.

I grew up in an old home with no insulation - it was cold sometimes to the point that there would be a bit of frost on the interior of the windows but never any condensation on the actual walls. The walls would feel quite cold as well.

Now I live in a high rise that has had water intrusion problems over the years and I have had walls that have been damaged and become moldy from the intrusion. I fixed my specific problem in my personal unit but that is specific to my construction which has soffits which were packed and waterproofed and flashed. Any water intrusion will now trickle into a neighbor's unit.

I would suspect there is some element of water intrusion to cause water as I also had significant efflorescensce caused by the intrusion and not by lack of insulation.

It could very well be lack of insulation in walls. My mom had a covered (roof only) patio added on to house. It must have disturbed the minimal insulation in that area and had some moisture/frost on the inside of that wall that winter, Minnesota, 1960 built house. The next summer they had insulation blown into the walls and that solved problem.

Only the landlord can really do something to correct. You might want to try hanging a heavy rug/tapestry on that section of wall to slightly insulate the area where the frost is. It might help. But do write a note to your LL to let them know about the problem, they may not know there is a problem, hopefully they care.