Cold temp, wet soil and low light is not a good combo for these plants. Seems you have some rotting going on on both plants. For the first pic (Euphorbia trigona?), I would cut down every affected stem down to soil level, with the hope the roots can be saved. If the base and roots feel mushy as well then I would try to save the healthy stems by cutting those off, let them callous and root them. Just making sure the cut part has healthy flesh only. Keep cutting higher up the stem if you still see rot where you cut.

Regarding the second pic (Pilosocereus?), rot seems to affect one stem at the growing point only. But one never knows it could also be going up within the stem all the way to the roots. I would cut the top of that stem out and keep cutting down the stem until you see heathy flesh only. In time that stem will put new growth, however your plant may look unsightly for some time. Alternatively, since you have multiple stem, you could just cut out the whole stem down to the soil level. It's also probably the safest way to save the plant if rot is indeed located solely in that stem.

Hopefully you will get more advises by others soon.

In second thoughts, it's difficult to determine from the pics whether it is rot or fungus infection. Could you tell whether the affected area feel soft/mushy to the touch

Alain, thank you so much for the reply. The cacti actually feel normal

Sorry for misleading you. Some stems on the trigona look greyish on the pic. Not sure what you mean by "look dead". Are they dried up, wrinkled or just discolored?

Regarding the second plant, this is likely fungus. You can treat with anti-fungus product but at the end of the day the plant will have a scar and you are also taking the risk of having the infection propagating to other stems and plants. So if it where mine, and since it is the growing tip that is affected, I would still cut of that stem in addition to treating the plant.